Factors of 259

How to find the factors of 259

Test every whole number from 1 up to the square root of 259 (√259 ≈ 16.093). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 259 ÷ 1 = 259 — so 1 and 259 are factors
• 259 ÷ 2 = 129.5 — not a whole number
• 259 ÷ 3 = 86.333 — not a whole number
• 259 ÷ 4 = 64.75 — not a whole number
• 259 ÷ 5 = 51.8 — not a whole number
• 259 ÷ 6 = 43.167 — not a whole number
• 259 ÷ 7 = 37 — so 7 and 37 are factors
• 259 ÷ 8 = 32.375 — not a whole number
• 259 ÷ 9 = 28.778 — not a whole number
• 259 ÷ 10 = 25.9 — not a whole number
• 259 ÷ 11 = 23.545 — not a whole number
• 259 ÷ 12 = 21.583 — not a whole number
• 259 ÷ 13 = 19.923 — not a whole number
• 259 ÷ 14 = 18.5 — not a whole number
• 259 ÷ 15 = 17.267 — not a whole number
• 259 ÷ 16 = 16.188 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 7, 37 and 259.

Prime factorization of 259

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

The primes you divided by give 259 = 7 × 37. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 259

• 259 is a composite number.
• The sum of all its factors is 304; the sum of its proper factors (excluding 259) is 45, which makes it a deficient number (its proper factors add up to less than itself).
• 259 is not a perfect square, so its factors pair up evenly.
• Multiples of 259 include 518, 777, 1,036, 1,295 and so on.

Factors vs. multiples

Factors of 259 are the numbers that divide into it; multiples of 259 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.