# Factors of 21 in pair

Factors of 21 in pair are (1, 21) , (3, 7)

#### How to find factors of a number in pair

 1.   Steps to find factors of 21 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 21 in pair

Factor Pair Pair Factorization
1 and 21 1 x 21 = 21
3 and 7 3 x 7 = 21

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 21. They are called negative pair factors.

Hence, the negative pairs of 21 would be ( -1 , -21 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 21 are 1 , 3 , 7 , 21. So, factors of 21 in pair are (1,21), (3,7).

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of Factors

• Every factor of a number is an exact divisor of that number, example 1, 3, 7, 21 are exact divisors of 21.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 21 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 21.

#### Steps to find Factors of 21

• Step 1. Find all the numbers that would divide 21 without leaving any remainder. Starting with the number 1 upto 10 (half of 21). The number 1 and the number itself are always factors of the given number.
21 ÷ 1 : Remainder = 0
21 ÷ 3 : Remainder = 0
21 ÷ 7 : Remainder = 0
21 ÷ 21 : Remainder = 0

Hence, Factors of 21 are 1, 3, 7, and 21

• Is 21 a composite number?

Yes 21 is a composite number.

• Is 21 a perfect square?

No 21 is not a perfect square.

• Write all odd factors of 21?

The factors of 21 are 1, 3, 7, 21.
Odd factors of 21 are 1 , 3 , 7 , 21.

• What is the mean of all prime factors of 21?

Factors of 21 are 1 , 3 , 7 , 21. Prime factors of 21 are 3 , 7. Therefore mean of prime factors of 21 is (3 + 7) / 2 = 5.00.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

#### Examples of Factors

Can you help Rubel in arranging 21 blocks in order to form a rectangle in all possible ways? For arranging 21 blocks in order to form a rectangle in all possible ways we need to find factors of 21 in pair.

Factors of 21 are 1, 3, 7, 21. So, factors of 21 in pair are (1,21), (3,7).

Ariel has been asked to write all factor pairs of 21 but she is finding it difficult. Can you help her find out?

Factors of 21 are 1, 3, 7, 21. So, factors of 21 in pair are (1,21), (3,7).

What are the pair factors of 21?

Factors of 21 are 1, 3, 7, 21. Hence, the factors of 21 in pair are (1,21), (3,7).

Can you help Sammy list the factors of 21 and also find the factor pairs?

Factors of 21 are 1, 3, 7, 21.
Factors of 21 in pair are (1,21), (3,7).

Help Diji in finding factors of 21 by Prime Factorization method and then sorting factors of 21 in pairs.

Prime factorization of 21 is 3 x 7. Factors of 21 in pair can be written as (1,21), (3,7).

Write the smallest prime factor of 21.

Smallest prime factor of 21 is 3.

Write the largest prime factor of 21.

Largest prime factor of 21 is 7.

Diji wants to write all the negative factors of 21. Can you help Diji in doing the same?

Negative factors of 21 are -1, -3, -7, -21.