Factors of 289

How to find the factors of 289

Test every whole number from 1 up to the square root of 289 (√289 ≈ 17.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 289 ÷ 1 = 289 — so 1 and 289 are factors
• 289 ÷ 2 = 144.5 — not a whole number
• 289 ÷ 3 = 96.333 — not a whole number
• 289 ÷ 4 = 72.25 — not a whole number
• 289 ÷ 5 = 57.8 — not a whole number
• 289 ÷ 6 = 48.167 — not a whole number
• 289 ÷ 7 = 41.286 — not a whole number
• 289 ÷ 8 = 36.125 — not a whole number
• 289 ÷ 9 = 32.111 — not a whole number
• 289 ÷ 10 = 28.9 — not a whole number
• 289 ÷ 11 = 26.273 — not a whole number
• 289 ÷ 12 = 24.083 — not a whole number
• 289 ÷ 13 = 22.231 — not a whole number
• 289 ÷ 14 = 20.643 — not a whole number
• 289 ÷ 15 = 19.267 — not a whole number
• 289 ÷ 16 = 18.063 — not a whole number
• 289 ÷ 17 = 17 — so 17 and 17 are factors

Collecting both numbers from every successful division gives the complete list: 1, 17 and 289.

Prime factorization of 289

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

The primes you divided by give 289 = 17². From the exponents you can also count the factors without listing them: (2 + 1) = 3.

Properties of 289

• 289 is a composite number.
• The sum of all its factors is 307; the sum of its proper factors (excluding 289) is 18, which makes it a deficient number (its proper factors add up to less than itself).
• 289 is a perfect square: 17 × 17. Perfect squares always have an odd number of factors.
• Multiples of 289 include 578, 867, 1,156, 1,445 and so on.

Factors vs. multiples

Factors of 289 are the numbers that divide into it; multiples of 289 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.