Factors of 125

How to find the factors of 125

Test every whole number from 1 up to the square root of 125 (√125 ≈ 11.180). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 125 ÷ 1 = 125 — so 1 and 125 are factors
• 125 ÷ 2 = 62.5 — not a whole number
• 125 ÷ 3 = 41.667 — not a whole number
• 125 ÷ 4 = 31.25 — not a whole number
• 125 ÷ 5 = 25 — so 5 and 25 are factors
• 125 ÷ 6 = 20.833 — not a whole number
• 125 ÷ 7 = 17.857 — not a whole number
• 125 ÷ 8 = 15.625 — not a whole number
• 125 ÷ 9 = 13.889 — not a whole number
• 125 ÷ 10 = 12.5 — not a whole number
• 125 ÷ 11 = 11.364 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 5, 25 and 125.

Prime factorization of 125

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

The primes you divided by give 125 = 5³. From the exponents you can also count the factors without listing them: (3 + 1) = 4.

Properties of 125

• 125 is a composite number.
• The sum of all its factors is 156; the sum of its proper factors (excluding 125) is 31, which makes it a deficient number (its proper factors add up to less than itself).
• 125 is not a perfect square, so its factors pair up evenly.
• 125 is also a perfect cube: 5³.
• Multiples of 125 include 250, 375, 500, 625 and so on.

Factors vs. multiples

Factors of 125 are the numbers that divide into it; multiples of 125 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.