Factors of 51

How to find the factors of 51

Test every whole number from 1 up to the square root of 51 (√51 ≈ 7.141). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 51 ÷ 1 = 51 — so 1 and 51 are factors
• 51 ÷ 2 = 25.5 — not a whole number
• 51 ÷ 3 = 17 — so 3 and 17 are factors
• 51 ÷ 4 = 12.75 — not a whole number
• 51 ÷ 5 = 10.2 — not a whole number
• 51 ÷ 6 = 8.5 — not a whole number
• 51 ÷ 7 = 7.286 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 17 and 51.

Prime factorization of 51

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

The primes you divided by give 51 = 3 × 17. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 51

• 51 is a composite number.
• The sum of all its factors is 72; the sum of its proper factors (excluding 51) is 21, which makes it a deficient number (its proper factors add up to less than itself).
• 51 is not a perfect square, so its factors pair up evenly.
• Multiples of 51 include 102, 153, 204, 255 and so on.

Factors vs. multiples

Factors of 51 are the numbers that divide into it; multiples of 51 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.