Factors of 60

How to find the factors of 60

Test every whole number from 1 up to the square root of 60 (√60 ≈ 7.746). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 60 ÷ 1 = 60 — so 1 and 60 are factors
• 60 ÷ 2 = 30 — so 2 and 30 are factors
• 60 ÷ 3 = 20 — so 3 and 20 are factors
• 60 ÷ 4 = 15 — so 4 and 15 are factors
• 60 ÷ 5 = 12 — so 5 and 12 are factors
• 60 ÷ 6 = 10 — so 6 and 10 are factors
• 60 ÷ 7 = 8.571 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

Prime factorization of 60

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

The primes you divided by give 60 = 2² × 3 × 5. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) = 12.

Properties of 60

• 60 is a composite number.
• The sum of all its factors is 168; the sum of its proper factors (excluding 60) is 108, which makes it a abundant number (its proper factors add up to more than itself).
• 60 is not a perfect square, so its factors pair up evenly.
• Multiples of 60 include 120, 180, 240, 300 and so on.

Factors vs. multiples

Factors of 60 are the numbers that divide into it; multiples of 60 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.