Factors of 961

How to find the factors of 961

Test every whole number from 1 up to the square root of 961 (√961 ≈ 31.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 961 ÷ 1 = 961 — so 1 and 961 are factors
• 961 ÷ 2 = 480.5 — not a whole number
• 961 ÷ 3 = 320.333 — not a whole number
• 961 ÷ 4 = 240.25 — not a whole number
• 961 ÷ 5 = 192.2 — not a whole number
• 961 ÷ 6 = 160.167 — not a whole number
• 961 ÷ 7 = 137.286 — not a whole number
• 961 ÷ 8 = 120.125 — not a whole number
• 961 ÷ 9 = 106.778 — not a whole number
• 961 ÷ 10 = 96.1 — not a whole number
• 961 ÷ 11 = 87.364 — not a whole number
• 961 ÷ 12 = 80.083 — not a whole number
• 961 ÷ 13 = 73.923 — not a whole number
• 961 ÷ 14 = 68.643 — not a whole number
• 961 ÷ 15 = 64.067 — not a whole number
• 961 ÷ 16 = 60.063 — not a whole number
• 961 ÷ 17 = 56.529 — not a whole number
• 961 ÷ 18 = 53.389 — not a whole number
• 961 ÷ 19 = 50.579 — not a whole number
• 961 ÷ 20 = 48.05 — not a whole number
• 961 ÷ 21 = 45.762 — not a whole number
• 961 ÷ 22 = 43.682 — not a whole number
• 961 ÷ 23 = 41.783 — not a whole number
• 961 ÷ 24 = 40.042 — not a whole number
• 961 ÷ 25 = 38.44 — not a whole number
• 961 ÷ 26 = 36.962 — not a whole number
• 961 ÷ 27 = 35.593 — not a whole number
• 961 ÷ 28 = 34.321 — not a whole number
• 961 ÷ 29 = 33.138 — not a whole number
• 961 ÷ 30 = 32.033 — not a whole number
• 961 ÷ 31 = 31 — so 31 and 31 are factors

Collecting both numbers from every successful division gives the complete list: 1, 31 and 961.

Prime factorization of 961

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

The primes you divided by give 961 = 31². From the exponents you can also count the factors without listing them: (2 + 1) = 3.

Properties of 961

• 961 is a composite number.
• The sum of all its factors is 993; the sum of its proper factors (excluding 961) is 32, which makes it a deficient number (its proper factors add up to less than itself).
• 961 is a perfect square: 31 × 31. Perfect squares always have an odd number of factors.
• Multiples of 961 include 1,922, 2,883, 3,844, 4,805 and so on.

Factors vs. multiples

Factors of 961 are the numbers that divide into it; multiples of 961 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.