# Factors of 972 in pair

Factors of 972 in pair are (1, 972) , (2, 486) , (3, 324) , (4, 243) , (6, 162) , (9, 108) , (12, 81) , (18, 54) and (27, 36)

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

 1.   Steps to find factors of 972 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 972 in pair

Factor Pair Pair Factorization
1 and 972 1 x 972 = 972
2 and 486 2 x 486 = 972
3 and 324 3 x 324 = 972
4 and 243 4 x 243 = 972
6 and 162 6 x 162 = 972
9 and 108 9 x 108 = 972
12 and 81 12 x 81 = 972
18 and 54 18 x 54 = 972
27 and 36 27 x 36 = 972

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 972. They are called negative pair factors.

Hence, the negative pairs of 972 would be ( -1 , -972 ) .

#### How do you define factor pairs of a number?

A factor pair of a number can be defined as the combination of two factors in such a way that when multiplied together produce the number itself. Every natural number is a product of atleast one factor pair. Eg- Factors of 972 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 81 , 108 , 162 , 243 , 324 , 486 , 972. So, factors of 972 in pair are (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 972 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 972.
• Every number is a factor of zero (0), since 972 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972 are exact divisors of 972.
• Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. Each factor divides 972 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972 are all less than or equal to 972.

#### Steps to find Factors of 972

• Step 1. Find all the numbers that would divide 972 without leaving any remainder. Starting with the number 1 upto 486 (half of 972). The number 1 and the number itself are always factors of the given number.
972 ÷ 1 : Remainder = 0
972 ÷ 2 : Remainder = 0
972 ÷ 3 : Remainder = 0
972 ÷ 4 : Remainder = 0
972 ÷ 6 : Remainder = 0
972 ÷ 9 : Remainder = 0
972 ÷ 12 : Remainder = 0
972 ÷ 18 : Remainder = 0
972 ÷ 27 : Remainder = 0
972 ÷ 36 : Remainder = 0
972 ÷ 54 : Remainder = 0
972 ÷ 81 : Remainder = 0
972 ÷ 108 : Remainder = 0
972 ÷ 162 : Remainder = 0
972 ÷ 243 : Remainder = 0
972 ÷ 324 : Remainder = 0
972 ÷ 486 : Remainder = 0
972 ÷ 972 : Remainder = 0

Hence, Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972

• Is 972 a composite number?

Yes 972 is a composite number.

• Is 972 a prime number?

No 972 is not a prime number.

• What is the mean of factors of 972?

Factors of 972 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 81 , 108 , 162 , 243 , 324 , 486 , 972. therefore mean of factors of 972 is (1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972) / 18 = 141.56.

• 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.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 972.
- Writing all prime factors of 972.
- Writing all the possible factors of 972 in pair.
Help him in writing all these.

Positive factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
Prime factors of 972 are 2, 2, 3, 3, 3, 3, 3.
Factors of 972 in pair are (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

What are the pair factors of 972?

Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972. Hence, the factors of 972 in pair are (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

Can you help Sammy list the factors of 972 and also find the factor pairs?

Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
Factors of 972 in pair are (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

The area of a rectangle is 972 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 972 in pair. So, the possible combinations (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

Help Diji in finding factors of 972 by Prime Factorization method and then sorting factors of 972 in pairs.

Prime factorization of 972 is 2 x 2 x 3 x 3 x 3 x 3 x 3. Factors of 972 in pair can be written as (1,972), (2,486), (3,324), (4,243), (6,162), (9,108), (12,81), (18,54), (27,36).

Write the smallest prime factor of 972.

Smallest prime factor of 972 is 2.

Write the largest prime factor of 972.

Largest prime factor of 972 is 3.

Diji wants to write all the negative factors of 972. Can you help Diji in doing the same?

Negative factors of 972 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -243, -324, -486, -972.