What Are the Factors of 56?
Fifty-six days is exactly 8 weeks, and 56 also splits into 7 groups of 8 or 4 groups of 14. Every one of those tidy splits is a factor: a whole number that divides another number exactly, with no remainder.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56. That is eight factors.
Factor Pairs of 56
Look for pairs that multiply to 56, working from the outside in.
- Start with 1 × 56.
- Try 2. Since 56 ÷ 2 = 28, write 2 × 28.
- Try 4. Since 56 ÷ 4 = 14, write 4 × 14.
- Try 7. Since 56 ÷ 7 = 8, write 7 × 8.
- Keep trying whole numbers until you reach 8, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 56
Prime factors show what 56 is built from. Split it and keep going until every branch is a prime.
So 56 = 2 × 2 × 2 × 7 = 2³ × 7. Its prime factors are 2 and 7. Add 1 to each exponent and multiply: (3 + 1) × (1 + 1) = 8, which matches the list.
Divisibility check for 56
A number divides by 56 when it divides by 7 and 8. Take 168: 168 ÷ 8 = 21 and 168 ÷ 7 = 24, so 168 is a multiple of 56.
Is 56 a Prime or Composite Number?
Composite. It has eight factors. The sum of all factors is 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120. The factors smaller than 56 add up to 64, which is more than 56, so 56 is called an abundant number.
Real-Life Uses of the Factors of 56
- Weeks. Fifty-six days is exactly 8 weeks.
- Crates. Fifty-six bottles fit in 7 crates of 8.
- Sharing. Fifty-six cards deal evenly to 2, 4, 7, 8 or 14 players.
Common Factors of 56 With Other Numbers
The factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70, so 56 and 70 share 1, 2, 7 and 14. The GCF is 14, which simplifies 56/70 to 4/5.
Quick Practice
Which of these are factors of 56: 5, 7 or 9? Only 7. Now try 63 and check it with the calculator.