Factors of 165

How to find the factors of 165

Test every whole number from 1 up to the square root of 165 (√165 ≈ 12.845). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 165 ÷ 1 = 165 — so 1 and 165 are factors
• 165 ÷ 2 = 82.5 — not a whole number
• 165 ÷ 3 = 55 — so 3 and 55 are factors
• 165 ÷ 4 = 41.25 — not a whole number
• 165 ÷ 5 = 33 — so 5 and 33 are factors
• 165 ÷ 6 = 27.5 — not a whole number
• 165 ÷ 7 = 23.571 — not a whole number
• 165 ÷ 8 = 20.625 — not a whole number
• 165 ÷ 9 = 18.333 — not a whole number
• 165 ÷ 10 = 16.5 — not a whole number
• 165 ÷ 11 = 15 — so 11 and 15 are factors
• 165 ÷ 12 = 13.75 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 5, 11, 15, 33, 55 and 165.

Prime factorization of 165

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

The primes you divided by give 165 = 3 × 5 × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) × (1 + 1) = 8.

Properties of 165

• 165 is a composite number.
• The sum of all its factors is 288; the sum of its proper factors (excluding 165) is 123, which makes it a deficient number (its proper factors add up to less than itself).
• 165 is not a perfect square, so its factors pair up evenly.
• Multiples of 165 include 330, 495, 660, 825 and so on.

Factors vs. multiples

Factors of 165 are the numbers that divide into it; multiples of 165 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.