Factors of 693

How to find the factors of 693

Test every whole number from 1 up to the square root of 693 (√693 ≈ 26.325). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 693 ÷ 1 = 693 — so 1 and 693 are factors
• 693 ÷ 2 = 346.5 — not a whole number
• 693 ÷ 3 = 231 — so 3 and 231 are factors
• 693 ÷ 4 = 173.25 — not a whole number
• 693 ÷ 5 = 138.6 — not a whole number
• 693 ÷ 6 = 115.5 — not a whole number
• 693 ÷ 7 = 99 — so 7 and 99 are factors
• 693 ÷ 8 = 86.625 — not a whole number
• 693 ÷ 9 = 77 — so 9 and 77 are factors
• 693 ÷ 10 = 69.3 — not a whole number
• 693 ÷ 11 = 63 — so 11 and 63 are factors
• 693 ÷ 12 = 57.75 — not a whole number
• 693 ÷ 13 = 53.308 — not a whole number
• 693 ÷ 14 = 49.5 — not a whole number
• 693 ÷ 15 = 46.2 — not a whole number
• 693 ÷ 16 = 43.313 — not a whole number
• 693 ÷ 17 = 40.765 — not a whole number
• 693 ÷ 18 = 38.5 — not a whole number
• 693 ÷ 19 = 36.474 — not a whole number
• 693 ÷ 20 = 34.65 — not a whole number
• 693 ÷ 21 = 33 — so 21 and 33 are factors
• 693 ÷ 22 = 31.5 — not a whole number
• 693 ÷ 23 = 30.13 — not a whole number
• 693 ÷ 24 = 28.875 — not a whole number
• 693 ÷ 25 = 27.72 — not a whole number
• 693 ÷ 26 = 26.654 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231 and 693.

Prime factorization of 693

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

The primes you divided by give 693 = 3² × 7 × 11. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) × (1 + 1) = 12.

Properties of 693

• 693 is a composite number.
• The sum of all its factors is 1,248; the sum of its proper factors (excluding 693) is 555, which makes it a deficient number (its proper factors add up to less than itself).
• 693 is not a perfect square, so its factors pair up evenly.
• Multiples of 693 include 1,386, 2,079, 2,772, 3,465 and so on.

Factors vs. multiples

Factors of 693 are the numbers that divide into it; multiples of 693 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.