Factors of 42

Understanding Prime and Composite Numbers When studying mathematics, one of the fundamental concepts that students learn is that of prime and composite numbers. In this article, we will delve into the factors of 42, a composite number, and explore the various ways in which it can be broken down into its component parts.

Factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42
Negative Factors of 42: -1, -2, -3, -6, -7, -14, -21 and -42
Prime Factors of 42: 2, 5
Prime Factorization of 42: 2 × 3 × 7
Factors of 42 in Pairs: (1, 42), (2, 21), (3, 14) and (6, 7)
Negative Pairs Factors of 42: (-1, -42), (-2, -21), (-3, -14) and (-6, -7)

Prime Numbers

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Some examples of prime numbers include 2, 3, 5, 7, and 11. Prime numbers are important in mathematics as they are used in many mathematical formulas and algorithms, and are also used in the study of number theory.

Composite Numbers

A composite number is a whole number greater than 1 that can be divided evenly by a number other than 1 or itself. In other words, a composite number is not a prime number. Some examples of composite numbers include 4, 6, 8, 9, and 10.

What are the factors of 42?

The method of calculating the factors of 42 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 42 are the factors of 42.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 42 ÷ 1 = 42

This division gives the remainder 0 and so is divisible by 42. So please put them 1 and 42 in your factor list.

1, …….. 42

(ii) 42 ÷ 2 = 21

This division gives the remainder 0 and so is divisible by 21. So please put them 2 and 21 in your factor list.

1, 2 …….. 21, 42

(iii) 42 ÷ 3 = 14

This division gives the remainder 0 and so is divisible by 14. So please put them 3 and 14 in your factor list.

1, 2, 3 …….. 14, 21, 42

(iv) 42 ÷ 4 = 10.5

This division gives the remainder 10.5, not being thoroughly divided. So we will not write 4 and 10.5 on the list.

(iv) 42 ÷ 5 = 8.4

This division gives the remainder 8.4, not being thoroughly divided. So we will not write 5 and 8.4 on the list.

(v) 42 ÷ 6 = 7

This division gives the remainder 0 and so is divisible by 7. So please put them 6 and 7 in your factor list.

1, 2, 3, 6 …….. 7, 14, 21, 42

(v) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 3, 6, 7, 14, 21, and 42 are factors of 42.

Factor pairs of 42

1 x 42 = 42
2 x 21 = 42
3 x 14 = 42
6 x 7 = 42

So, (1, 42), (2, 21), (3, 14) and (6, 7) are factor pairs of 42

Factor pairs of -42

-1 x -42 = 42
-2 x -21 = 42
-3 x -14 = 42
-6 x -7 = 42

So, (-1, -42), (-2, -21), (-3, -14) and (-6, -7) are negative pair factors of 42

Prime Factorization of 42

42 ÷ 2 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1

Therefore, 2 × 3 × 7 are Prime factorization of 42.

Factor tree of 42

         42
        /  \
       2    21 
           /  \
          3    7