Factors of 66

How to find the factors of 66

Test every whole number from 1 up to the square root of 66 (√66 ≈ 8.124). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 66 ÷ 1 = 66 — so 1 and 66 are factors
• 66 ÷ 2 = 33 — so 2 and 33 are factors
• 66 ÷ 3 = 22 — so 3 and 22 are factors
• 66 ÷ 4 = 16.5 — not a whole number
• 66 ÷ 5 = 13.2 — not a whole number
• 66 ÷ 6 = 11 — so 6 and 11 are factors
• 66 ÷ 7 = 9.429 — not a whole number
• 66 ÷ 8 = 8.25 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 6, 11, 22, 33 and 66.

Prime factorization of 66

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

The primes you divided by give 66 = 2 × 3 × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 66

• 66 is a composite number.
• The sum of all its factors is 144; the sum of its proper factors (excluding 66) is 78, which makes it a abundant number (its proper factors add up to more than itself).
• 66 is not a perfect square, so its factors pair up evenly.
• Multiples of 66 include 132, 198, 264, 330 and so on.

Factors vs. multiples

Factors of 66 are the numbers that divide into it; multiples of 66 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.