Factors of number 42 are the pair of numbers which, when multiplied together gives the original number. There are other composite numbers such as 48, 60, 70, 420, 36, 45, 30, etc. whose factors and prime factorisation can be determined. We can find the factors of a number of 42 in a very simple and easy method. It involves the multiplication of a pair of numbers to get another number. In this article, we will learn the factors of 42, and the pair factors and the prime factors of 42 using the prime factorization method with many solved examples.
Table of Contents:
What are the Factors of 42?
The factors of 42 are the numbers that divide 42 exactly without remainder. As the number 42 is a composite number, it has many factors other than one and the number itself. The factors of 42 can be positive or negative, but it cannot be in decimal or fraction form. Therefore, the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
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Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42. Prime Factorization of 42: 2 × 3 × 7 |
Pair Factors of 42
We can find the factors in pairs for 42, by multiplying two numbers in a combination to get the result as 42. This can be done as follows:
1 × 42 = 42
2 × 21 = 42
3 × 14 = 42
6 × 7 = 42
Therefore, the factors of 42 in pairs are (1, 42), (2, 21), (3, 14) and (6, 7).
Prime Factorization of 42
The number 42 is a composite number. Now let us find the prime factors of 42.
- The first step is to divide the number 42 with the smallest prime factor, i.e. 2.
42 ÷ 2 = 21
- Now, check whether 21 can be further divided by 2 or not.
21 ÷ 2 = 10.5
But, a factor cannot be a fraction. Therefore, we will proceed to the next prime number, which is 3.
- Now, dividing 21 by 3 we get,
21 ÷ 3 = 7
- Again, dividing 7 by 3 will give a fraction number. Therefore, taking the next prime number, 5, into consideration.
21 ÷ 5 = 4.2, again a fraction number.
So the next prime number is 7.
7 ÷ 7 = 1
- We have received 1 at the end and further, we cannot proceed with the division method, as we know the multiple of 1 is 1 only. So, the prime factors of 42 are 2 × 3 × 7, where 2, 3 and 7 are prime numbers.
Video Lesson on Prime Factors
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| Factor Theorem | Prime Factors |
Examples
Example 1:
Find the common factors of 42 and 41.
Solution:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
The factors of 41 are 1 and 41.
As the number 41 is a prime number, the common factor of 42 and 41 is 1.
Example 2:
Find the common factors of 42 and 43.
Solution:
Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42.
Factors of 43 = 1 and 43.
Thus, the common factor of 42 and 43 is 1.
Example 3:
Find the common factors of 42 and 44.
Solution:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
The factors of 44 are 1, 2, 4, 11, 22, 44.
Therefore, the common factors of 42 and 44 are 1 and 2.
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Frequently Asked Questions on Factors of 42
What are the factors of 42?
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
What is the prime factorization of 42?
The prime factorization of 42 is 2 × 3 × 7.
Write down the positive pair factors of 42.
The positive pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).
What are the negative pair factors of 42?
The negative pair factors of 42 are (-1, -42), (-2, -21), (-3, -14), and (-6, -7).
Is 21 a factor of 42?
Yes, 21 is a factor of 42. As 21 divides 42 exactly, and hence 21 is a factor of 42.
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