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Factors of 972

Factors of 972 are integers that can be divided evenly into 972. There are overall 18 factors of 972 among which 972 is the biggest factor and 2, 3 are its prime factors. The sum of all factors of 972 is 2548.

  • All Factors of 972: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486 and 972
  • Prime Factors of 972: 2, 3
  • Prime Factorization of 972: 22 × 35
  • Sum of Factors of 972: 2548
1. What Are the Factors of 972?
2. Factors of 972 by Prime Factorization
3. Factors of 972 in Pairs
4. FAQs on Factors of 972
Factors of 972

What are Factors of 972?

Factors of 972 are pairs of those numbers whose products result in 972. These factors are either prime numbers or composite numbers.

How to Find the Factors of 972?

To find the factors of 972, we will have to find the list of numbers that would divide 972 without leaving any remainder.

  • 972/1 = 972; therefore, 1 is a factor of 972.
  • 972/18 = 54; therefore, 18 is a factor of 972.
Similarly we can find other factors. Hence, the factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.

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Factors of 972 by Prime Factorization

The number 972 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 972. The first step is to divide the number 972 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 972 ÷ 2 = 486
  • 486 ÷ 2 = 243

Further dividing 243 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 243 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 972 can be written as 22 × 35 where 2, 3 are prime.

 

Factors of 972 in Pairs

Pair factors of 972 are the pairs of numbers that when multiplied give the product 972. The factors of 972 in pairs are:

  • 1 × 972 = (1, 972)
  • 2 × 486 = (2, 486)
  • 3 × 324 = (3, 324)
  • 4 × 243 = (4, 243)
  • 6 × 162 = (6, 162)
  • 9 × 108 = (9, 108)
  • 12 × 81 = (12, 81)
  • 18 × 54 = (18, 54)
  • 27 × 36 = (27, 36)

Negative pair factors of 972 are:

  • -1 × -972 = (-1, -972)
  • -2 × -486 = (-2, -486)
  • -3 × -324 = (-3, -324)
  • -4 × -243 = (-4, -243)
  • -6 × -162 = (-6, -162)
  • -9 × -108 = (-9, -108)
  • -12 × -81 = (-12, -81)
  • -18 × -54 = (-18, -54)
  • -27 × -36 = (-27, -36)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 972 Solved Examples

  1. Example 1: How many factors are there for 972?

    Solution:

    The factors of 972 are too many, therefore if we can find the prime factorization of 972, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 972 = 22 × 35
    Therefore, the total number of factors are (2 + 1) × (5 + 1) = 3 × 6 = 18

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 972 and 131.

    Solution:

    The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972 and factors of 131 are 1, 131.

    Therefore, the Least Common Multiple (LCM) of 972 and 131 is 127332 and Greatest Common Factor (GCF) of 972 and 131 is 1.

  3. Example 3: Find if 1, 2, 3, 6, 9, 18, 324 and 856 are factors of 972.

    Solution:

    When we divide 972 by 856 it leaves a remainder. Therefore, the number 856 is not a factor of 972. All numbers except 856 are factors of 972.

  4. Example 4: Find the product of all the prime factors of 972.

    Solution:

    Since, the prime factors of 972 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.

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FAQs on Factors of 972

What are the 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 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -243, -324, -486, -972.

What is the Sum of all the Factors of 972?

Sum of all factors of 972 = (22 + 1 - 1)/(2 - 1) × (35 + 1 - 1)/(3 - 1) = 2548

What Numbers are the Prime Factors of 972?

The prime factors of 972 are 2, 3.

What is the Greatest Common Factor of 972 and 699?

The factors of 972 and 699 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972 and 1, 3, 233, 699 respectively.

Common factors of 972 and 699 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 972 and 699 is 3.

What are the Common Factors of 972 and 731?

Since, the factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972 and factors of 731 are 1, 17, 43, 731. Hence, 972 and 731 have only one common factor which is 1. Therefore, 972 and 731 are co-prime.

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