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Factors of 42

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Last updated date: 19th Mar 2024
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What are the Factors of 42?

Factors are an important concept in arithmetic. Factors of 42 are simply numbers — more than two, which upon multiplication lead to the result or product of 42. In simple terms, factors are two or more numbers which upon multiplication lead to another number.  Factors are also explored in algebra. Since algebra uses variables most of the time, the factors of an algebraic term are also in the form of variables.


The example below can explain this further:


(x2 + 5x + 5) is an algebraic term with two factors (x+5) and (x+ 1)

(x+5)(x+ 1) = x2 + 5x + 5


Know the Factors of 42

Factors of 42 are simply numbers, more than two, which upon multiplication lead to the result or product of 42. Other important concepts for solving for factors are prime numbers, multiplication tables up to 20, negative and positive numbers.


Let's discover the factors of 42 through the division method. 


Starting from the smallest number, let's find the common factors 42 by division method:

42 ÷ 1 = 42

42 ÷ 2 = 21

42 ÷ 3 = 14

42 ÷ 4 = not divisible

42 ÷ 5 = not divisible

42 ÷ 6 = 7

42 ÷ 7 = 6

42 ÷ 8 = not divisible

42 ÷ 9 = not divisible

42 ÷ 10 = not divisible

42 ÷ 11 = not divisible

42 ÷ 12 = not divisible

42 ÷ 13 = not divisible

42 ÷ 14 = not divisible

42 ÷ 15 = not divisible

42 ÷ 16 = not divisible

42 ÷ 17 = not divisible

42 ÷ 18 = not divisible

42 ÷ 19 = not divisible

42 ÷ 20 = not divisible


Following the multiplication tables up to 20, we can easily find the factors of 42. 


The factors of 42 obtained are 42, 21, 14, 7, and 6.


In order to know more factors of 42, we can start dividing 42 with the factors that we have obtained until now. 


42 ÷ 42 = 1

42 ÷ 21 = 2

42 ÷ 14 = 3

42 ÷ 7 = 6

42 ÷ 6 = 7


With the above method, we have found 3 more new factors of 42 that are 1, 2, and 3. The common factors for 42 are 6 and 7. 


Therefore the total number of factors that 42 has is 8 and they are 1, 2, 3, 6, 7, 14, 21, and 42.


Pairs of factors is another approach of finding factors of a number. The pairs of factors for 42 can be derived from the single factors that we have found above: 1, 2, 3, 6, 7, 14, 21, and 42.


Use the approach below in order to understand the methodology behind a pair of two factors:


1 x 42 = 42

2 x 21 = 42

3 x 14 = 42

6 x 7 = 42


From the calculation above, it can be inferred that there are 4 pairs of two factors for 42. They are (1, 42), (2 x 21), (3 x 14) and (6x 7). You can observe that these pairs of factors have been derived originally from the factors obtained through division. Therefore, it is highly recommended that you use the division approach when attempting questions on factors.


Just as there are pairs of two factors, there are also pairs of three and more factors for a product. This approach is used to find the smallest factors of 42. Similar to pairs of two factors, we will be using the factors derived from the division method: 1, 2, 3, 6, 7, 14, 21, and 42.


2 x 3 x 7 = 42

1 x 2 x 21 = 42

1 x 3 x 14 = 42

1 x 6 x 7 = 42


From the calculations above, we can see that there can be a pair of three factors for 42, and they are  (2, 3, 7), (1, 2, 21), (1, 3, 14), and (1, 6, 7).


Factors can also be positive and negative numbers. This means that a positive product can also be due to the multiplication of two negative factors. By simply adding the negative sign for each factor, you can get a positive product with negative factors. It can be put as follow:


-1 x -42 = 42

-2 x -21 = 42

-3 x -14 = 42

-6 x -7 = 42


Therefore the factors for 42 can also be a pair of two factors such as (-1, -42), (-2, -21), (-3, -14) and (-6, -7)


Prime Factorization of 42

The number 42 is made up of several different numbers. Let's look for 42's prime factors now.

  • The first step is to divide 42 by the smallest prime factor, which is two.

42 ÷ 2 = 2

  • Check to see if 21 can be split by two more times.

10.5 + 2 = 21

A factor, on the other hand, cannot be a fraction. As a result, we'll move on to the next prime number, which is three.

  • Now, if we divide 21 by 3, we get

21 ÷ 3 = 7

  • Divide 7 by 3 to get a fraction number once more. As a result, evaluate the next prie number, 5, as well.

Again, a fraction number, 21 5 = 4.2.

So 7 is the next prime number.

7 ÷ 7 = 1

  • We've got 1 at the end, and we can't use the division approach because we know the multiple of 1 is only 1. 2 3 7 are the prime factors of 42, with 2, 3 and 7 being prime numbers.

FAQs on Factors of 42

1. What is factorization?

Factorization is the process of breaking down a large number into smaller numbers that, when multiplied together, return the original value. Factorization of the number 12 can look like 3 times 4 for example. When you reduce a number to prime factors, you can further break it down using prime factorization. The factorisation is the process of lowering a quadratic equation's bracket rather than expanding it and transforming the equation to a product of factors that can't be lowered anymore.

2. What is the greatest factor of 42?

Factors are usually smaller than the product since they are a multiplication of numbers that result in another number. A number itself is its greatest factor. The biggest factor for 42 is 42 itself. The factor's value is never greater than the product's value. You can learn about the factorisation of the number 42 with the help of the free PDF of Factors of 42 by Vedantu. The simple and easy to read language can help students to know about the factorisation of the number 42 in a simpler manner.

3. How can we use the Prime Factorization Method to find the factors of 42?

A prime number is a number that is the product of 1 and the number itself. 2 is a prime number which is the product of 1 and 2 (the number itself). It's important to remember that 1 is not a prime number. Other prime numbers are 3, 5, 7, and so on. There are no other components in these numbers save 1 and the number itself. 2 x 3 x 7 = 42 is the prime factorization of 42.Factors of 42 are specifically unique in their nature. Some major lessons from the PDF include understanding its elements through division and prime factorization.

4. What is the factorisation formula?

The factorization formula divides a large integer into smaller parts, called factors. A factor is a number that entirely divides an integer without leaving any remainder. A given value's factorization formula can be written as a factorization formula. Here it is when N is any number, X, Y, and Z are number factors, and a, b, and c are the exponents of factors X, Y, and Z, respectively. N= X x Yx Z. You can learn about the factorisation formula with the help of experts at Vedantu. 

5. How is the free PDF of Factors of 42 helpful?

The free PDF of Factors of 42 is very helpful. It is given in a simple to read and understand manner that can help students to know about the factorisation of the number 42. You will be able to understand the factors of 42 and solve the factorisation by using simple methods. It can be complex for some students and you are required to acknowledge the topic with the help of experts at Vedantu.