Factors of 689

How to find the factors of 689

Test every whole number from 1 up to the square root of 689 (√689 ≈ 26.249). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 689 ÷ 1 = 689 — so 1 and 689 are factors
• 689 ÷ 2 = 344.5 — not a whole number
• 689 ÷ 3 = 229.667 — not a whole number
• 689 ÷ 4 = 172.25 — not a whole number
• 689 ÷ 5 = 137.8 — not a whole number
• 689 ÷ 6 = 114.833 — not a whole number
• 689 ÷ 7 = 98.429 — not a whole number
• 689 ÷ 8 = 86.125 — not a whole number
• 689 ÷ 9 = 76.556 — not a whole number
• 689 ÷ 10 = 68.9 — not a whole number
• 689 ÷ 11 = 62.636 — not a whole number
• 689 ÷ 12 = 57.417 — not a whole number
• 689 ÷ 13 = 53 — so 13 and 53 are factors
• 689 ÷ 14 = 49.214 — not a whole number
• 689 ÷ 15 = 45.933 — not a whole number
• 689 ÷ 16 = 43.063 — not a whole number
• 689 ÷ 17 = 40.529 — not a whole number
• 689 ÷ 18 = 38.278 — not a whole number
• 689 ÷ 19 = 36.263 — not a whole number
• 689 ÷ 20 = 34.45 — not a whole number
• 689 ÷ 21 = 32.81 — not a whole number
• 689 ÷ 22 = 31.318 — not a whole number
• 689 ÷ 23 = 29.957 — not a whole number
• 689 ÷ 24 = 28.708 — not a whole number
• 689 ÷ 25 = 27.56 — not a whole number
• 689 ÷ 26 = 26.5 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 13, 53 and 689.

Prime factorization of 689

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

The primes you divided by give 689 = 13 × 53. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.

Properties of 689

• 689 is a composite number.
• The sum of all its factors is 756; the sum of its proper factors (excluding 689) is 67, which makes it a deficient number (its proper factors add up to less than itself).
• 689 is not a perfect square, so its factors pair up evenly.
• Multiples of 689 include 1,378, 2,067, 2,756, 3,445 and so on.

Factors vs. multiples

Factors of 689 are the numbers that divide into it; multiples of 689 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.