Factors of 217

How to find the factors of 217

Test every whole number from 1 up to the square root of 217 (√217 ≈ 14.731). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 217 ÷ 1 = 217 — so 1 and 217 are factors
• 217 ÷ 2 = 108.5 — not a whole number
• 217 ÷ 3 = 72.333 — not a whole number
• 217 ÷ 4 = 54.25 — not a whole number
• 217 ÷ 5 = 43.4 — not a whole number
• 217 ÷ 6 = 36.167 — not a whole number
• 217 ÷ 7 = 31 — so 7 and 31 are factors
• 217 ÷ 8 = 27.125 — not a whole number
• 217 ÷ 9 = 24.111 — not a whole number
• 217 ÷ 10 = 21.7 — not a whole number
• 217 ÷ 11 = 19.727 — not a whole number
• 217 ÷ 12 = 18.083 — not a whole number
• 217 ÷ 13 = 16.692 — not a whole number
• 217 ÷ 14 = 15.5 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 7, 31 and 217.

Prime factorization of 217

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

The primes you divided by give 217 = 7 × 31. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 217

• 217 is a composite number.
• The sum of all its factors is 256; the sum of its proper factors (excluding 217) is 39, which makes it a deficient number (its proper factors add up to less than itself).
• 217 is not a perfect square, so its factors pair up evenly.
• Multiples of 217 include 434, 651, 868, 1,085 and so on.

Factors vs. multiples

Factors of 217 are the numbers that divide into it; multiples of 217 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.