Factors of 42

Definition of factors of 42: If a number completely divides 42 without leaving a remainder, then that number is called a factor of 42.

By the above definition, we can say that the factors of 42 are the divisors of 42. In this section, we will learn about the factors of 42 and the prime factors of 42.

Also Read: Basic concepts of factors

Highlights of Factors of 42

  • 42 = 2×3×7 is the prime factorization of 42.
  • The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
  • The prime factors of 42 are 2, 3 and 7.
  • Negative factors of 42 are –1, -2, -3, -6, -7, -14, -21 and –42.

What are the factors of 42?

Let us write the number 42 multiplicatively in all possible ways. We have:

42 = 1×42 

42 = 2×21

42 = 3×14

42 = 6×7

We cannot write 42 multiplicatively in any other way than the above ones, so we will stop right now. Thus the factors of 42 in pairs are given as follows:

42 = a×b Factors in Pairs (a,b)
42 = 1×42  (1, 42)
42 = 2×21 (2, 21)
42 = 3×14 (3, 14)
42 = 6×7 (6, 7)

Thus the pair factors of 42 are (1, 42), (2, 21), (3, 14) and (6, 7). As all the numbers appearing in pair factors are the factors of 42, we conclude that

The factors of 42 are:

1, 2, 3, 6, 7, 14, 21 and 42.

Number of factors of 42

From above we have calculated the factors of 42 which are 1, 2, 3, 6, 7, 14, 21 and 42. Thus the total number of factors of 42 is eight.

Prime Factors of 42

Note that the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Among those factors, we observe that only 2, 3 and 7 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 42 are 2, 3 and 7.

Question: What are the factors of 42?

Video Solution:

How to find factors of 42?

Now we will determine the factors of 42 by division method. In this method, we will try to find the numbers that can divide 42 with no remainder. See that

42/1=42 and the remainder is 0.

1 and 42 are factors of 42.

42/2=18 and the remainder is 0.

2 and 21 are factors of 42.

42/3=14 and the remainder is 0.

3 and 14 are factors of 42.

42/6=7 and the remainder is 0.

6 and 7 are factors of 42.

Note that no numbers other than the numbers in violet color can divide 42. So the numbers in violet color, that is, 1, 2, 3, 6, 7, 14, 21 and 42 are the complete list of factors of 42.