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Factors of 924

Factors of 924 are numbers that, when multiplied in pairs give the product as 924. There are 24 factors of 924, of which the following are its prime factors 2, 3, 7, 11. The Prime Factorization of 924 is 22 × 31 × 71 × 111.

  • All Factors of 924: 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462 and 924
  • Prime Factors of 924: 2, 3, 7, 11
  • Prime Factorization of 924: 22 × 31 × 71 × 111
  • Sum of Factors of 924: 2688
1. What Are the Factors of 924?
2. Factors of 924 by Prime Factorization
3. Factors of 924 in Pairs
4. FAQs on Factors of 924
Factors of 924

What are Factors of 924?

Factors of 924 are pairs of those numbers whose products result in 924. These factors are either prime numbers or composite numbers.

How to Find the Factors of 924?

To find the factors of 924, we will have to find the list of numbers that would divide 924 without leaving any remainder.

  • 924/66 = 14; therefore, 66 is a factor of 924 and 14 is also a factor of 924.
  • 924/4 = 231; therefore, 4 is a factor of 924 and 231 is also a factor of 924.
Similarly we can find other factors. Hence, the factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924.

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Factors of 924 by Prime Factorization

The number 924 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 924. The first step is to divide the number 924 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 924 ÷ 2 = 462
  • 462 ÷ 2 = 231

Further dividing 231 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 231 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 924 can be written as 22 × 31 × 71 × 111 where 2, 3, 7, 11 are prime.

 

Factors of 924 in Pairs

Pair factors of 924 are the pairs of numbers that when multiplied give the product 924. The factors of 924 in pairs are:

  • 1 × 924 = (1, 924)
  • 2 × 462 = (2, 462)
  • 3 × 308 = (3, 308)
  • 4 × 231 = (4, 231)
  • 6 × 154 = (6, 154)
  • 7 × 132 = (7, 132)
  • 11 × 84 = (11, 84)
  • 12 × 77 = (12, 77)
  • 14 × 66 = (14, 66)
  • 21 × 44 = (21, 44)
  • 22 × 42 = (22, 42)
  • 28 × 33 = (28, 33)

Negative pair factors of 924 are:

  • -1 × -924 = (-1, -924)
  • -2 × -462 = (-2, -462)
  • -3 × -308 = (-3, -308)
  • -4 × -231 = (-4, -231)
  • -6 × -154 = (-6, -154)
  • -7 × -132 = (-7, -132)
  • -11 × -84 = (-11, -84)
  • -12 × -77 = (-12, -77)
  • -14 × -66 = (-14, -66)
  • -21 × -44 = (-21, -44)
  • -22 × -42 = (-22, -42)
  • -28 × -33 = (-28, -33)

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

Factors of 924 Solved Examples

  1. Example 1: How many factors are there for 924?

    Solution:

    The factors of 924 are too many, therefore if we can find the prime factorization of 924, 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 924 = 22 × 31 × 71 × 111
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24

  2. Example 2: Find the LCM and Highest Common Factor (HCF) of 924 and 64.

    Solution:

    The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924 and factors of 64 are 1, 2, 4, 8, 16, 32, 64.

    Therefore, the LCM of 924 and 64 is 14784 and Highest Common Factor (HCF) of 924 and 64 is 4.

  3. Example 3: Find if 14, 22, 42, 66, 77, 84, 231 and 561 are factors of 924.

    Solution:

    When we divide 924 by 561 it leaves a remainder. Therefore, the number 561 is not a factor of 924. All numbers except 561 are factors of 924.

  4. Example 4: Find the product of all the prime factors of 924.

    Solution:

    Since, the prime factors of 924 are 2, 3, 7, 11. Therefore, the product of prime factors = 2 × 3 × 7 × 11 = 462.

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FAQs on Factors of 924

What are the Factors of 924?

The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924 and its negative factors are -1, -2, -3, -4, -6, -7, -11, -12, -14, -21, -22, -28, -33, -42, -44, -66, -77, -84, -132, -154, -231, -308, -462, -924.

What is the Sum of all the Factors of 924?

Sum of all factors of 924 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 2688

What are Prime Factors of 924?

The prime factors of 924 are 2, 3, 7, 11.

What is the Greatest Common Factor of 924 and 221?

The factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924 and the factors of 221 are 1, 13, 17, 221. 924 and 221 have only one common factor which is 1. This implies that 924 and 221 are co-prime.

Hence, the Greatest Common Factor (GCF) of 924 and 221 is 1.

How Many Factors of 924 are also Factors of 194?

Since, the factors of 924 are 1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924 and the factors of 194 are 1, 2, 97, 194.
Hence, [1, 2] are the common factors of 924 and 194.

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