Factors of 112

How to find the factors of 112

Test every whole number from 1 up to the square root of 112 (√112 ≈ 10.583). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 112 ÷ 1 = 112 — so 1 and 112 are factors
• 112 ÷ 2 = 56 — so 2 and 56 are factors
• 112 ÷ 3 = 37.333 — not a whole number
• 112 ÷ 4 = 28 — so 4 and 28 are factors
• 112 ÷ 5 = 22.4 — not a whole number
• 112 ÷ 6 = 18.667 — not a whole number
• 112 ÷ 7 = 16 — so 7 and 16 are factors
• 112 ÷ 8 = 14 — so 8 and 14 are factors
• 112 ÷ 9 = 12.444 — not a whole number
• 112 ÷ 10 = 11.2 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.

Prime factorization of 112

Divide by the smallest prime that fits, and keep going until the quotient is 1:

The primes you divided by give 112 = 2⁴ × 7. From the exponents you can also count the factors without listing them: (4 + 1) × (1 + 1) = 10.

Properties of 112

• 112 is a composite number.
• The sum of all its factors is 248; the sum of its proper factors (excluding 112) is 136, which makes it a abundant number (its proper factors add up to more than itself).
• 112 is not a perfect square, so its factors pair up evenly.
• Multiples of 112 include 224, 336, 448, 560 and so on.

Factors vs. multiples

Factors of 112 are the numbers that divide into it; multiples of 112 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.