Factors of 21

Factors of 21 are those numbers that, when multiplied together, give the result of 21. We can also say that a factor is a number that divides a number ultimately, leaving zero as a remainder. We will use the multiplication method to find the factors of 21.

Factors of 21

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Factors of 21: 1, 3, 7 and 21
Factors of -21: -1, -3, -7 and -21
Prime Factors of 21: 3, 7
Prime Factorization of 21: 3 × 7
Factors of 21 in Pairs: (1, 21) and (3, 7)

What are the factors of 21?

The method of calculating the factors of 21 is as follows. First, each number can be divided by one and by itself.

Consequently, 1 and 21 are the factors of 21.
By dividing a number by 1, 2, 3, 4… we can discover all its factors.

(i) 21 ÷ 1 = 21

This division gives the remainder 0 and so is divisible by 21. So please put them 1 and 21 in your factor list.

1, …….. 21

(ii) 21 ÷ 2 = 10.5

This division gives the remainder 10.5, not being thoroughly divided. So we will not write 2 and 10.5 on the list.

(iii) 21 ÷ 3 = 7

This division gives the remainder 0 and so is divisible by 7. So please put them 3 and 7 in your factor list.

1, 3 …….. 7, 21

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

So 1, 3, 7 and 21 are factors of 21.

Factors of 21

Factors of -21

To get the factors of -21 by the multiplication method, we will first write the number -21 multiplicatively in all possible ways. We can write -21 as follows and we have:

21 = -1 × -21 Therefore, -1, -21 are factors of -21
21 = -3 × -7 Therefore, -3, -7 are factors of -21

As there are no other ways we can express -21 multiplicative, we will stop now, and we have obtained all the factors of -21.

So, the factors of -21 are -1, -3, -7 and -21

All factors of 21

Here is a list of all the positive and negative factors of 21 in numerical order.

1, 3, 7, 21, -1, -3, -7 and -21

Therefore, 1, 3, 7, 21, -1, -3, -7 and -21 are All factors of 21.

Factor pairs of 21

21 x 1 = 21
3 x 7 = 21

So, (1, 21) and (3, 70) are factor pairs of 21

Prime Factorization of 21

21 ÷ 3 = 7
7 ÷ 7 = 1

Therefore, 3 × 7 are the Prime factorization of 21.

Factor tree of 21

         21
        /   \
      3      7

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