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Q:

# What are the factors of 96?

A:

The whole-number factors of the number 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. The opposite or negative of each of the represented numbers is also a factor of 96. These numbers are factors because each can be multiplied by a specific integer to produce 96.

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The factors of a number like 96 can be most easily found through division. Each number (or divisor) divided by 96 that creates an integer quotient is a factor of 96, as is the quotient.

96/1 = 96, so 1 and 96 are factors;

96/2 = 48, so 2 and 48 are factors;

96/3 = 32, so 3 and 32 are factors;

96/4 = 24, so 4 and 24 are factors;

94/6 = 16, so 6 and 16 are factors;

94/8 = 12, so 8 and 12 are factors.

The other numbers in between 1 and 12 (5, 7, 9, 10, 11) could not be perfectly divided. There is no need to test number 12 and above.

Prime factorization splits a number into its prime number factors. For 96, the only prime factors are 2 and 3, but five factors of 2 must be multiplied by 3. For example, 2*2*2*2*2*3 = 96, which can also be expressed as (2^5)*3 = 96, or 32*3 = 96.

Factors and multiples are closely associated because the larger number is one multiple of each of its factors. Factoring would help a person find the greatest common factor or least common multiple of 96 and another number.

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