Factors of 672

How to find the factors of 672

Test every whole number from 1 up to the square root of 672 (√672 ≈ 25.923). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 672 ÷ 1 = 672 — so 1 and 672 are factors
• 672 ÷ 2 = 336 — so 2 and 336 are factors
• 672 ÷ 3 = 224 — so 3 and 224 are factors
• 672 ÷ 4 = 168 — so 4 and 168 are factors
• 672 ÷ 5 = 134.4 — not a whole number
• 672 ÷ 6 = 112 — so 6 and 112 are factors
• 672 ÷ 7 = 96 — so 7 and 96 are factors
• 672 ÷ 8 = 84 — so 8 and 84 are factors
• 672 ÷ 9 = 74.667 — not a whole number
• 672 ÷ 10 = 67.2 — not a whole number
• 672 ÷ 11 = 61.091 — not a whole number
• 672 ÷ 12 = 56 — so 12 and 56 are factors
• 672 ÷ 13 = 51.692 — not a whole number
• 672 ÷ 14 = 48 — so 14 and 48 are factors
• 672 ÷ 15 = 44.8 — not a whole number
• 672 ÷ 16 = 42 — so 16 and 42 are factors
• 672 ÷ 17 = 39.529 — not a whole number
• 672 ÷ 18 = 37.333 — not a whole number
• 672 ÷ 19 = 35.368 — not a whole number
• 672 ÷ 20 = 33.6 — not a whole number
• 672 ÷ 21 = 32 — so 21 and 32 are factors
• 672 ÷ 22 = 30.545 — not a whole number
• 672 ÷ 23 = 29.217 — not a whole number
• 672 ÷ 24 = 28 — so 24 and 28 are factors
• 672 ÷ 25 = 26.88 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336 and 672.

Prime factorization of 672

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

The primes you divided by give 672 = 2⁵ × 3 × 7. From the exponents you can also count the factors without listing them: (5 + 1) × (1 + 1) × (1 + 1) = 24.

Properties of 672

• 672 is a composite number.
• The sum of all its factors is 2,016; the sum of its proper factors (excluding 672) is 1,344, which makes it a abundant number (its proper factors add up to more than itself).
• 672 is not a perfect square, so its factors pair up evenly.
• Multiples of 672 include 1,344, 2,016, 2,688, 3,360 and so on.

Factors vs. multiples

Factors of 672 are the numbers that divide into it; multiples of 672 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.