Factors of 216

How to find the factors of 216

Test every whole number from 1 up to the square root of 216 (√216 ≈ 14.697). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 216 ÷ 1 = 216 — so 1 and 216 are factors
• 216 ÷ 2 = 108 — so 2 and 108 are factors
• 216 ÷ 3 = 72 — so 3 and 72 are factors
• 216 ÷ 4 = 54 — so 4 and 54 are factors
• 216 ÷ 5 = 43.2 — not a whole number
• 216 ÷ 6 = 36 — so 6 and 36 are factors
• 216 ÷ 7 = 30.857 — not a whole number
• 216 ÷ 8 = 27 — so 8 and 27 are factors
• 216 ÷ 9 = 24 — so 9 and 24 are factors
• 216 ÷ 10 = 21.6 — not a whole number
• 216 ÷ 11 = 19.636 — not a whole number
• 216 ÷ 12 = 18 — so 12 and 18 are factors
• 216 ÷ 13 = 16.615 — not a whole number
• 216 ÷ 14 = 15.429 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108 and 216.

Prime factorization of 216

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

The primes you divided by give 216 = 2³ × 3³. From the exponents you can also count the factors without listing them: (3 + 1) × (3 + 1) = 16.

Properties of 216

• 216 is a composite number.
• The sum of all its factors is 600; the sum of its proper factors (excluding 216) is 384, which makes it a abundant number (its proper factors add up to more than itself).
• 216 is not a perfect square, so its factors pair up evenly.
• 216 is also a perfect cube: 6³.
• Multiples of 216 include 432, 648, 864, 1,080 and so on.

Factors vs. multiples

Factors of 216 are the numbers that divide into it; multiples of 216 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.