Factors of 169

How to find the factors of 169

Test every whole number from 1 up to the square root of 169 (√169 ≈ 13.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 169 ÷ 1 = 169 — so 1 and 169 are factors
• 169 ÷ 2 = 84.5 — not a whole number
• 169 ÷ 3 = 56.333 — not a whole number
• 169 ÷ 4 = 42.25 — not a whole number
• 169 ÷ 5 = 33.8 — not a whole number
• 169 ÷ 6 = 28.167 — not a whole number
• 169 ÷ 7 = 24.143 — not a whole number
• 169 ÷ 8 = 21.125 — not a whole number
• 169 ÷ 9 = 18.778 — not a whole number
• 169 ÷ 10 = 16.9 — not a whole number
• 169 ÷ 11 = 15.364 — not a whole number
• 169 ÷ 12 = 14.083 — not a whole number
• 169 ÷ 13 = 13 — so 13 and 13 are factors

Collecting both numbers from every successful division gives the complete list: 1, 13 and 169.

Prime factorization of 169

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

The primes you divided by give 169 = 13². From the exponents you can also count the factors without listing them: (2 + 1) = 3.

Properties of 169

• 169 is a composite number.
• The sum of all its factors is 183; the sum of its proper factors (excluding 169) is 14, which makes it a deficient number (its proper factors add up to less than itself).
• 169 is a perfect square: 13 × 13. Perfect squares always have an odd number of factors.
• Multiples of 169 include 338, 507, 676, 845 and so on.

Factors vs. multiples

Factors of 169 are the numbers that divide into it; multiples of 169 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.