# Factors of 972

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

#### How to find factors of a number

 1.   Find factors of 972 using Division Method 2.   Find factors of 972 using Prime Factorization 3.   Find factors of 972 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 972

• Divide 972 by 1: 972 ÷ 1 : Remainder = 0
• Divide 972 by 2: 972 ÷ 2 : Remainder = 0
• Divide 972 by 3: 972 ÷ 3 : Remainder = 0
• Divide 972 by 4: 972 ÷ 4 : Remainder = 0
• Divide 972 by 6: 972 ÷ 6 : Remainder = 0
• Divide 972 by 9: 972 ÷ 9 : Remainder = 0
• Divide 972 by 12: 972 ÷ 12 : Remainder = 0
• Divide 972 by 18: 972 ÷ 18 : Remainder = 0
• Divide 972 by 27: 972 ÷ 27 : Remainder = 0
• Divide 972 by 36: 972 ÷ 36 : Remainder = 0
• Divide 972 by 54: 972 ÷ 54 : Remainder = 0
• Divide 972 by 81: 972 ÷ 81 : Remainder = 0
• Divide 972 by 108: 972 ÷ 108 : Remainder = 0
• Divide 972 by 162: 972 ÷ 162 : Remainder = 0
• Divide 972 by 243: 972 ÷ 243 : Remainder = 0
• Divide 972 by 324: 972 ÷ 324 : Remainder = 0
• Divide 972 by 486: 972 ÷ 486 : Remainder = 0
• Divide 972 by 972: 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

#### 2. Steps to find factors of 972 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 972 using the division method, follow these steps:

• Step 1. Start dividing 972 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 972, which is 2. Divide 972 by 2 to obtain the quotient (486).
972 ÷ 2 = 486
• Step 3. Repeat step 1 with the obtained quotient (486).
486 ÷ 2 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 972 is, 972 = 2 x 2 x 3 x 3 x 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 972 as shown below:

So, the prime factorization of 972 is, 972 = 2 x 2 x 3 x 3 x 3 x 3 x 3.

#### 3. Find factors of 972 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 972 would be the two numbers which, when multiplied, give 972 as the result.

The following table represents the calculation of factors of 972 in pairs:

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 ) , ( -2 , -486 ) , ( -3 , -324 ) , ( -4 , -243 ) , ( -6 , -162 ) , ( -9 , -108 ) , ( -12 , -81 ) , ( -18 , -54 ) and ( -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.

• Which is the smallest prime factor of 972?

Smallest prime factor of 972 is 2.

• Is 972 a perfect square?

No 972 is not a perfect square.

• What are five multiples of 972?

First five multiples of 972 are 1944, 2916, 3888, 4860, 5832.

• What is prime factorization of 972?

Prime factorization of 972 is 2 x 2 x 3 x 3 x 3 x 3 x 3.

• What are 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.

• How do you find factors of a negative number? ( eg. -972 )?

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

• Is 972 a whole number?

Yes 972 is a whole number.

• Which is greatest factor of 972?

The greatest factor of 972 is 486.

• What are the prime factors of 972?

The 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.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 972. Can you help her?

Prime factors of 972 are 2, 2, 3, 3, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even 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.
Even factors of 972 are 2, 4, 6, 12, 18, 36, 54, 108, 162, 324, 486, 972.
Hence, product of even factors of 972 is; 2 x 4 x 6 x 12 x 18 x 36 x 54 x 108 x 162 x 324 x 486 x 972 = 53973124931819670000.

Joy wants to calculate mean of all the factors of 972. Help him in finding the mean of 972.

Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 972 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972 = 2548.
Hence, the mean of factors of 972 is 2548 ÷ 18 = 141.56.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 972? Help her in writing all the factors.

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

How many factors are there for 972?

Factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
So there are in total 18 factors.

Joey wants to write all the prime factors of 972 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 972 are 2, 2, 3, 3, 3, 3, 3.
So in exponential form it can be written as 22 x 35.

Kevin has been asked to write 17 factor(s) of 972. Can you predict the answer?

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