Factors of 42 With Examples
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.
What are the Factors of Forty Two?
The factors of Forty Two 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 Forty Two can be positive or negative, but it cannot be in decimal or fraction form. Therefore, the factors of Forty Two are 1, 2, 3, 6, 7, 14, 21 and 42.
Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42. Prime Factorization of 42: 2 × 3 × 7 |
Pair Factors of Forty Two
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 Forty Two are 2 × 3 × 7, where 2, 3 and 7 are prime numbers.
Examples
Example 1:
Find the common factors of Forty Two 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 Forty Two and 41 is 1.
Example 2:
Find the common factors of Forty Two and 43.
Solution:
Factors of Forty Two = 1, 2, 3, 6, 7, 14, 21 and 42.
Factors of 43 = 1 and 43.
Thus, the common factor of Forty Two and 43 is 1.
Frequently Asked Questions on Factors of Forty Two
Q1 What are the factors of Forty Two?
Ans. The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Q2 What is the prime factorization of 42?
Ans. The prime factorization of 42 is 2 × 3 × 7.
Q3 Write down the positive pair factors of Forty Two.
Ans. The positive pair factors of Forty Two are (1, 42), (2, 21), (3, 14), and (6, 7).
Q4 What are the negative pair factors of Forty Two?
Ans. The negative pair factors of Forty Two are (-1, -42), (-2, -21), (-3, -14), and (-6, -7).
Q5 Is 21 a factor of Forty Two?
Ans. Yes, 21 is a factor of Forty Two. As 21 divides 42 exactly, and hence 21 is a factor of Forty Two.
Category: Maths