Factors of 768

How to find the factors of 768

Test every whole number from 1 up to the square root of 768 (√768 ≈ 27.713). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

• 768 ÷ 1 = 768 — so 1 and 768 are factors
• 768 ÷ 2 = 384 — so 2 and 384 are factors
• 768 ÷ 3 = 256 — so 3 and 256 are factors
• 768 ÷ 4 = 192 — so 4 and 192 are factors
• 768 ÷ 5 = 153.6 — not a whole number
• 768 ÷ 6 = 128 — so 6 and 128 are factors
• 768 ÷ 7 = 109.714 — not a whole number
• 768 ÷ 8 = 96 — so 8 and 96 are factors
• 768 ÷ 9 = 85.333 — not a whole number
• 768 ÷ 10 = 76.8 — not a whole number
• 768 ÷ 11 = 69.818 — not a whole number
• 768 ÷ 12 = 64 — so 12 and 64 are factors
• 768 ÷ 13 = 59.077 — not a whole number
• 768 ÷ 14 = 54.857 — not a whole number
• 768 ÷ 15 = 51.2 — not a whole number
• 768 ÷ 16 = 48 — so 16 and 48 are factors
• 768 ÷ 17 = 45.176 — not a whole number
• 768 ÷ 18 = 42.667 — not a whole number
• 768 ÷ 19 = 40.421 — not a whole number
• 768 ÷ 20 = 38.4 — not a whole number
• 768 ÷ 21 = 36.571 — not a whole number
• 768 ÷ 22 = 34.909 — not a whole number
• 768 ÷ 23 = 33.391 — not a whole number
• 768 ÷ 24 = 32 — so 24 and 32 are factors
• 768 ÷ 25 = 30.72 — not a whole number
• 768 ÷ 26 = 29.538 — not a whole number
• 768 ÷ 27 = 28.444 — not a whole number

Collecting both numbers from every successful division gives the complete list: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384 and 768.

Prime factorization of 768

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

The primes you divided by give 768 = 2⁸ × 3. From the exponents you can also count the factors without listing them: (8 + 1) × (1 + 1) = 18.

Properties of 768

• 768 is a composite number.
• The sum of all its factors is 2,044; the sum of its proper factors (excluding 768) is 1,276, which makes it a abundant number (its proper factors add up to more than itself).
• 768 is not a perfect square, so its factors pair up evenly.
• Multiples of 768 include 1,536, 2,304, 3,072, 3,840 and so on.

Factors vs. multiples

Factors of 768 are the numbers that divide into it; multiples of 768 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.