What Are the Factors of 96?
A big box of 96 crayons can be laid out in 8 rows of 12, 6 rows of 16 or 4 rows of 24. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96. That is twelve factors.
Factor Pairs of 96
Look for pairs that multiply to 96, working from the outside in.
- Start with 1 × 96.
- Try 2. Since 96 ÷ 2 = 48, write 2 × 48.
- Try 3. Since 96 ÷ 3 = 32, write 3 × 32.
- Try 4. Since 96 ÷ 4 = 24, write 4 × 24.
- Try 6. Since 96 ÷ 6 = 16, write 6 × 16.
- Try 8. Since 96 ÷ 8 = 12, write 8 × 12.
- Keep trying whole numbers until you reach 12, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 96
Prime factors show what 96 is built from. Split it and keep going until every branch is a prime.
So 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3. Its prime factors are 2 and 3. Add 1 to each exponent and multiply: (5 + 1) × (1 + 1) = 12, which matches the list.
Divisibility check for 96
A number divides by 96 when it divides by 32 and 3. Take 288: 288 ÷ 32 = 9, and its digits add up to 18, so 288 is a multiple of 96.
Is 96 a Prime or Composite Number?
Composite. It has twelve factors. The sum of all factors is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 16 + 24 + 32 + 48 + 96 = 252. The factors smaller than 96 add up to 156, which is more than 96, so 96 is called an abundant number.
Real-Life Uses of the Factors of 96
- Crayons. A box of 96 crayons fits in 8 rows of 12.
- Eggs. Ninety-six eggs make exactly 8 dozen.
- Hours. Ninety-six hours is exactly 4 days.
Common Factors of 96 With Other Numbers
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144, so 96 and 144 share 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48. The GCF is 48, which simplifies 96/144 to 2/3.
Quick Practice
Which of these are factors of 96: 5, 6 or 9? Only 6. Now try 105 and check it with the calculator.