Factors of 231

How to find the factors of 231

Test every whole number from 1 up to the square root of 231 (√231 ≈ 15.199). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 231 ÷ 1 = 231 — so 1 and 231 are factors
• 231 ÷ 2 = 115.5 — not a whole number
• 231 ÷ 3 = 77 — so 3 and 77 are factors
• 231 ÷ 4 = 57.75 — not a whole number
• 231 ÷ 5 = 46.2 — not a whole number
• 231 ÷ 6 = 38.5 — not a whole number
• 231 ÷ 7 = 33 — so 7 and 33 are factors
• 231 ÷ 8 = 28.875 — not a whole number
• 231 ÷ 9 = 25.667 — not a whole number
• 231 ÷ 10 = 23.1 — not a whole number
• 231 ÷ 11 = 21 — so 11 and 21 are factors
• 231 ÷ 12 = 19.25 — not a whole number
• 231 ÷ 13 = 17.769 — not a whole number
• 231 ÷ 14 = 16.5 — not a whole number
• 231 ÷ 15 = 15.4 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 7, 11, 21, 33, 77 and 231.

Prime factorization of 231

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

The primes you divided by give 231 = 3 × 7 × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 231

• 231 is a composite number.
• The sum of all its factors is 384; the sum of its proper factors (excluding 231) is 153, which makes it a deficient number (its proper factors add up to less than itself).
• 231 is not a perfect square, so its factors pair up evenly.
• Multiples of 231 include 462, 693, 924, 1,155 and so on.

Factors vs. multiples

Factors of 231 are the numbers that divide into it; multiples of 231 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.