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Factors of 864

Factors of 864 are the list of integers that we can split evenly into 864. There are total 24 factors of 864, of which 2, 3 are its prime factors. The Prime Factorization of 864 is 25 × 33.

  • All Factors of 864: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432 and 864
  • Prime Factors of 864: 2, 3
  • Prime Factorization of 864: 25 × 33
  • Sum of Factors of 864: 2520
1. What Are the Factors of 864?
2. Factors of 864 by Prime Factorization
3. Factors of 864 in Pairs
4. FAQs on Factors of 864
Factors of 864

What are Factors of 864?

Factors of 864 are pairs of those numbers whose products result in 864. These factors are either prime numbers or composite numbers.

How to Find the Factors of 864?

To find the factors of 864, we will have to find the list of numbers that would divide 864 without leaving any remainder.

  • 864/16 = 54; therefore, 16 is a factor of 864 and 54 is also a factor of 864.
  • 864/36 = 24; therefore, 36 is a factor of 864 and 24 is also a factor of 864.
Similarly we can find other factors. Hence, the factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.

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Factors of 864 by Prime Factorization

The number 864 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 864. The first step is to divide the number 864 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 864 ÷ 2 = 432
  • 432 ÷ 2 = 216
  • 216 ÷ 2 = 108
  • 108 ÷ 2 = 54
  • 54 ÷ 2 = 27

Further dividing 27 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 27 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 864 can be written as 25 × 33 where 2, 3 are prime.

 

Factors of 864 in Pairs

Pair factors of 864 are the pairs of numbers that when multiplied give the product 864. The factors of 864 in pairs are:

  • 1 × 864 = (1, 864)
  • 2 × 432 = (2, 432)
  • 3 × 288 = (3, 288)
  • 4 × 216 = (4, 216)
  • 6 × 144 = (6, 144)
  • 8 × 108 = (8, 108)
  • 9 × 96 = (9, 96)
  • 12 × 72 = (12, 72)
  • 16 × 54 = (16, 54)
  • 18 × 48 = (18, 48)
  • 24 × 36 = (24, 36)
  • 27 × 32 = (27, 32)

Negative pair factors of 864 are:

  • -1 × -864 = (-1, -864)
  • -2 × -432 = (-2, -432)
  • -3 × -288 = (-3, -288)
  • -4 × -216 = (-4, -216)
  • -6 × -144 = (-6, -144)
  • -8 × -108 = (-8, -108)
  • -9 × -96 = (-9, -96)
  • -12 × -72 = (-12, -72)
  • -16 × -54 = (-16, -54)
  • -18 × -48 = (-18, -48)
  • -24 × -36 = (-24, -36)
  • -27 × -32 = (-27, -32)

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

Factors of 864 Solved Examples

  1. Example 1: How many factors are there for 864?

    Solution:

    The factors of 864 are too many, therefore if we can find the prime factorization of 864, 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 864 = 25 × 33
    Therefore, the total number of factors are (5 + 1) × (3 + 1) = 6 × 4 = 24

  2. Example 2: Find the LCM and Highest Common Factor (HCF) of 864 and 217.

    Solution:

    The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864 and factors of 217 are 1, 7, 31, 217.

    Therefore, the LCM of 864 and 217 is 187488 and Highest Common Factor (HCF) of 864 and 217 is 1.

  3. Example 3: Find if 1, 2, 4, 12, 24, 108, 494 and 864 are factors of 864.

    Solution:

    When we divide 864 by 494 it leaves a remainder. Therefore, the number 494 is not a factor of 864. All numbers except 494 are factors of 864.

  4. Example 4: Find the product of all the prime factors of 864.

    Solution:

    Since, the prime factors of 864 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.

Show Solution >

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FAQs on Factors of 864

What are the Factors of 864?

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -96, -108, -144, -216, -288, -432, -864.

What is the Sum of all the Factors of 864?

Sum of all factors of 864 = (25 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) = 2520

What are the Pair Factors of 864?

The pair factors of 864 are (1, 864), (2, 432), (3, 288), (4, 216), (6, 144), (8, 108), (9, 96), (12, 72), (16, 54), (18, 48), (24, 36), (27, 32).

What is the Greatest Common Factor of 864 and 487?

The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864 and the factors of 487 are 1, 487. 864 and 487 have only one common factor which is 1. This implies that 864 and 487 are co-prime.

Hence, the Greatest Common Factor (GCF) of 864 and 487 is 1.

What are the Common Factors of 864 and 706?

Since, the factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864 and the factors of 706 are 1, 2, 353, 706.
Hence, [1, 2] are the common factors of 864 and 706.

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