What Are the Factors of 112?
One hundred twelve days is exactly 16 weeks, and 112 also splits into 7 groups of 16 or 8 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 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112. That is ten factors.
Factor Pairs of 112
Look for pairs that multiply to 112, working from the outside in.
- Start with 1 × 112.
- Try 2. Since 112 ÷ 2 = 56, write 2 × 56.
- Try 4. Since 112 ÷ 4 = 28, write 4 × 28.
- Try 7. Since 112 ÷ 7 = 16, write 7 × 16.
- Try 8. Since 112 ÷ 8 = 14, write 8 × 14.
- Keep trying whole numbers until you reach 14, which is already in your list. Every factor is now found, so you are done.
Prime Factorization of 112
Prime factors show what 112 is built from. Split it and keep going until every branch is a prime.
So 112 = 2 × 2 × 2 × 2 × 7 = 2⁴ × 7. Its prime factors are 2 and 7. Add 1 to each exponent and multiply: (4 + 1) × (1 + 1) = 10, which matches the list.
Divisibility check for 112
A number divides by 112 when it divides by 16 and 7. Take 336: 336 ÷ 16 = 21 and 336 ÷ 7 = 48, so 336 is a multiple of 112.
Is 112 a Prime or Composite Number?
Composite. It has ten factors. The sum of all factors is 1 + 2 + 4 + 7 + 8 + 14 + 16 + 28 + 56 + 112 = 248. The factors smaller than 112 add up to 136, which is more than 112, so 112 is called an abundant number.
Real-Life Uses of the Factors of 112
- Weeks. 112 days is exactly 16 weeks.
- Pallets. 112 tins stack as 7 layers of 16.
- Sharing. 112 cards deal evenly to 2, 4, 7, 8, 14 or 16 players.
Common Factors of 112 With Other Numbers
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70 and 140, so 112 and 140 share 1, 2, 4, 7, 14 and 28. The GCF is 28, which simplifies 112/140 to 4/5.
Quick Practice
Which of these are factors of 112: 5, 7 or 9? Only 7. Now try 128 and check it with the calculator.