42 as a product of prime factors

In other words it is finding which prime numbers should be multiplied together to make 72. We will use the same method as before to find its factors. We have done the prime factorization. Can you help her in finding the correct answer? To think of it the other way round, factors are the numbers multiplied to make another number exactly. . Similarly, the following is the list of the positive factors of 42. is the process that focuses on dividing an integer into its prime factors until the result is 1. The positive pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7). Your email address will not be published. Explore factors using illustrations and interactive examples: Factor pairs are the two numbers which, when multiplied, give the number 42. Factors of a number are the numbers which divide the given number exactly without leaving any remainder. Hence, the factors of 135 are 1, 3, 5, 9, 15, 27, 45 and 135. The final answer is the product of the prime numbers displayed at the end of these branches. Example - Write 140 as the Product of Its Prime Factors. The same is true for 9, 10, 11, 12, and 13. The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420 because all these numbers divide the number 420 evenly. Since the product of two negative numbers is positive, i.e. Such that, the set of numbers that produce 42 as their result will be termed as the proposed factors of the number 42. Again, dividing 7 by 3 will give a fraction number. 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Find its smallest prime factor: it is divisible by 2. Fundamental to number theory are whole numbers: 0, 1, 2, 3, and so on. The following image shows the factor tree of the number 42, The geometrical portrayal of the factors of 42 is shown by its. The sum of all factors of 350 is 744. 8 21 4 = 42, does this mean 8 and 21 4 are factors of 42? It lets us look at the building blocks of a number before they are combined. Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300. Lets look at a bigger number, 196. The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Here, the quotient obtained on division is also a factor of 420. Can you help him in finding the correct answer? 2 is prime, so circle it and leave it alone. Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42. Let us express 42 in terms of the product of its prime factors. of that natural number. 2 is a factor because 196 is even. We first defined basic factors, then thought about prime and proper factors too. Unfortunately, your teacher wont give many marks if you put 42 as the answer to everything in your next test! Factors of 42 | ProtonsTalk If this number is divisible by 4, the original number is, If the last digit is 0 or 5, the number is divisible by 5, If the number is divisible by 2 and 3 using the above rules, it is also divisible by 6. The second divisor in each pair is found by dividing the original number by the pairs first divisor. Therefore, sum of factors of 420 are 1 + 2 + 3 + 4 + 5 + 6 + 7 + 10 + 12 + 14 + 15 + 20 + 21 + 28 + 30 + 35 + 42 + 60 + 70 + 84 + 105 + 140 + 210 + 420 = 1344. A prime factor is a positive integer that can only be divided by 1 and itself. Your Mobile number and Email id will not be published. Created by Sal Khan and Monterey Institute for Technology and Education. These are the pairs that multiply to make 42: If the rules were bent a little and included negative numbers, there would be another 8 divisors. In the rest of this lesson, were going to take an in-depth look at how we found this out and lots more about factors. The number 42 is a composite number. 7? Answer To verify which product is the prime factorization of 18, we must check two things: that the product is equal to 18 and that the factors in the product are all prime numbers. A factor is the same a divisor: a number that divides another number exactly, without leaving a remainder. Prime Factors of 42 are all the prime numbers that when multiplied together equal 42. 98 is not prime, so you must factorize it. Factors of 42 are basically the numbers that divide it evenly or exactly without leaving any remainder i.e if a number divides 42 with a remainder of zero, then that number is called a factor. Medium Solution Verified by Toppr 42=237 Explanation: The lowest prime number is 2. Check for the remainder. In the following article, we will learn about the factors of 420 and the methodology to find these factors. However, 21 is divisible by numbers other than 1 and itself, so divide it by its smallest prime factor, 3: We substitute our factorization of 21 into our factorization of 42 to give a single equation: Your final two challenges for this lesson are to find all the factors of a much bigger number yourself. 2 2 3 2. We stop the division when we reach 1. But, only 2 people can be accommodated on each table. We stated the factors of 42 and found a fool-proof method to find the factors of any number. 422=21 Now 21 cannot be divided by 2 so we now divide by the next highest prime number which is 3. We will also look at a harder example to give you the confidence to solve problems alone. 40 as a Product of Prime Factors - Visual Fractions Save my name, email, and website in this browser for the next time I comment. Prime factorization (video) | Khan Academy 42 is an interesting number! whose factors and prime factorisation can be determined. Therefore, the number of desserts served is 420. of 42. The prime factorization of 420 can be represented by using a factor tree as shown below: So, the prime factorization of 420 is 420 = 2 x 2 x 3 x 5 x 7. Since we are finding the prime factors of 42, they will be placed as the roots of our factor tree. Therefore, taking the next prime number, 5, into consideration. number 7, present on the right side of the image) and the numbers mentioned in the left column (i.e. The following is the list of the negative factors of 42. Factors of 42 are the list of positive and negative whole numbers that can be divided evenly into 42. Therefore, the common factors of 42 and 44 are 1 and 2. 42 = 237. How do you write 42 as a product of its prime factors? Integers or numbers that can only be divided equally by themselves and by one are known as, . Do you get the same answer? Can you help him in finding the correct answer? Factors of 135 | How to Find the Prime Factors of 135 by the Prime The factors of the given number are shown in each row of the factor tree, but the well-defined set of prime factors for the number 42 is formed by the combination of the final known factor (i.e. This is not true for square numbers their square root is a factor that is happy by itself! 2, 3). Finding LCM and HCF from prime factors - Prime factors - BBC The pair of factors can be both a set of. If the number 420 is divided by a natural number such that the remainder is zero, then the natural number is known as a factor of 420. The number 42 is a composite number because 42 can be divided by 1, by itself and at least by 2, 3 and 7. Tim had to list the factors of 42 and 60 and find the common factors between them. Stop counting when you reach The square root of N. We hope youve enjoyed todays topic and feel confident in factoring numbers. number 7, present on the right side of the image) and the numbers mentioned in the left column (i.e. How to find the product of prime factors? We can do this using the division method or by using a factor tree. Complete step-by-step answer: Can you draw the factor tree with 6 and 7 as the branches? The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42 and the factors of 6 are 1, 2, 3, and 6. Prime Factorization by Upside-Down Division. Ali misplaced the list of factors of 42 and is unable to find the H.C.F of the factors of 42. 7 is a prime number. Its pair is (4, 8) and multiplying them gives: The numbers in a pair are different, most of the time. Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. For Valentines day, the restaurant offered a special discount on desserts, where each table receives an extra dessert for free on ordering one. This means that a numbers proper factors are also in the category of its regular factors as above. Composite numbers are numbers that have more than two factors. Factors of 42 and How to Find Them Matter of Math Viola! Enter a natural number to get its fator tree: Look at the 2 factors and determine if at least one of them is not prime; Repeat this process until all factors are prime. In this lesson, we will calculate the factors of 42, its prime factors, and its factors in pairs. We only need to write down 14 once. There are multiple pairs that will do this e.g. Write 24 as the product of its prime factors NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions Class 11 Business Studies, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 8 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions For Class 6 Social Science, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, CBSE Previous Year Question Papers Class 12 Maths, CBSE Previous Year Question Papers Class 10 Maths, ICSE Previous Year Question Papers Class 10, ISC Previous Year Question Papers Class 12 Maths, JEE Advanced 2023 Question Paper with Answers, JEE Main 2023 Question Papers with Answers, JEE Main 2022 Question Papers with Answers, JEE Advanced 2022 Question Paper with Answers. 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 4, If a natural number can be expressed as a product of prime numbers, these prime numbers are known as the. The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Note that the number \({1}\) is not used within a factor tree. Numbers that arent squares have an even amount they are all in pairs with numbers different to themselves. Factors Of 48 Factors of 48 are the numbers that give the original number when multiplied together in pairs or we can say, the numbers which divide 48 completely, leaving zero as a remainder, are its factors. Prime Factorization of 42: 2 3 7 We will look at the finding these in more detail below. remainder is left behind, therefore, the number 1 is referred to as a well-defined factor of 42. integer factors. Keep practicing, and leave a comment if you have any questions or a good fact about 42! Prime factors are important because they are the basic building blocks of all integers remember that every integer can be written uniquely as a product of prime factors! The prime factorization of the number 42 is given as follows. Write 40 as a product of its prime factors. The number 42 is significant and is an even composite number which means that it has several factors, in this case, 42 has 8 factors. If the sum is divisible by 3, the original number is, Just look at the last two digits. So the prime decomposition of 196 is: Try this again, but this time choose a different pair to start with. However, its important to get the method right on small numbers before moving on to a bigger challenge! A cube has all multiplicities divisible by 3 (it is of the form a3 for some a ). All integers are either even or odd. Thus, the common factor of 42 and 43 is 1. From the list, it can be seen that the H.C.F (Highest Common Factor) of the factors of 42 is the number. It involves the multiplication of a pair of numbers to get another number. Continue using the previously mentioned procedure to divide 42 by the other set of integers. 2 70, 4 35, 5 28 etc, but it doesn't matter which one we choose. Finding prime factors Prime factors are factors of a number that are, themselves, prime numbers. 98 we have to keep dividing it by prime numbers 98 is an even number so we can first divide by 2 98 / 2 = 49 49 is a multiple of 7 which too is a prime number so we can divide 49 by 7 49/7 = 7 7 can be divided again by 1 7/7 = 1 98 is divisible by 2 and 7 A factoris the same a divisor: a number that divides another number exactly, without leaving a remainder. Frequently Asked Questions on Factors of 420. hat divide 420 without leaving any remainder. Therefore, the greatest common factor of 420 and 150 is 30. How to Write a Number as a Product of Its Prime Factors , divide the number completely, without leaving any, behind. A prime number is a number that is only divisible by itself and one. When a composite number is written as a product of all of its prime factors, we have the prime factorization of the number. Now, lets start the division of 42 by the different sets of integers. See our other factor lessons: Factors of 56 Factors of 100, Your email address will not be published. The Fundamental Theorem of Arithmetic states that every . Hence, the common factors of 42 and 60 are 1, 2, 3 and 6. Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42 similarly factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. of a numbers prime factors is a factor tree.