Factors of 224

How to find the factors of 224

Test every whole number from 1 up to the square root of 224 (√224 ≈ 14.967). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 224 ÷ 1 = 224 — so 1 and 224 are factors
• 224 ÷ 2 = 112 — so 2 and 112 are factors
• 224 ÷ 3 = 74.667 — not a whole number
• 224 ÷ 4 = 56 — so 4 and 56 are factors
• 224 ÷ 5 = 44.8 — not a whole number
• 224 ÷ 6 = 37.333 — not a whole number
• 224 ÷ 7 = 32 — so 7 and 32 are factors
• 224 ÷ 8 = 28 — so 8 and 28 are factors
• 224 ÷ 9 = 24.889 — not a whole number
• 224 ÷ 10 = 22.4 — not a whole number
• 224 ÷ 11 = 20.364 — not a whole number
• 224 ÷ 12 = 18.667 — not a whole number
• 224 ÷ 13 = 17.231 — not a whole number
• 224 ÷ 14 = 16 — so 14 and 16 are factors

Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112 and 224.

Prime factorization of 224

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

The primes you divided by give 224 = 2⁵ × 7. From the exponents you can also count the factors without listing them: (5 + 1) × (1 + 1) = 12.

Properties of 224

• 224 is a composite number.
• The sum of all its factors is 504; the sum of its proper factors (excluding 224) is 280, which makes it a abundant number (its proper factors add up to more than itself).
• 224 is not a perfect square, so its factors pair up evenly.
• Multiples of 224 include 448, 672, 896, 1,120 and so on.

Factors vs. multiples

Factors of 224 are the numbers that divide into it; multiples of 224 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.