How to find the factors of 68
Test every whole number from 1 up to the square root of 68 (√68 ≈ 8.246). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 68 ÷ 1 = 68 — so 1 and 68 are factors
- 68 ÷ 2 = 34 — so 2 and 34 are factors
- 68 ÷ 3 = 22.667 — not a whole number
- 68 ÷ 4 = 17 — so 4 and 17 are factors
- 68 ÷ 5 = 13.6 — not a whole number
- 68 ÷ 6 = 11.333 — not a whole number
- 68 ÷ 7 = 9.714 — not a whole number
- 68 ÷ 8 = 8.5 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 2, 4, 17, 34 and 68.
Prime factorization of 68
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 68 = 2² × 17. From the exponents you can also count the factors without listing them: (2 + 1) × (1 + 1) = 6.
Properties of 68
- 68 is a composite number.
- The sum of all its factors is 126; the sum of its proper factors (excluding 68) is 58, which makes it a deficient number (its proper factors add up to less than itself).
- 68 is not a perfect square, so its factors pair up evenly.
- Multiples of 68 include 136, 204, 272, 340 and so on.
Factors vs. multiples
Factors of 68 are the numbers that divide into it; multiples of 68 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.
Frequently asked questions
What are the factors of 68?
The factors of 68 are 1, 2, 4, 17, 34 and 68. Each of these divides 68 with no remainder.
How many factors does 68 have?
68 has 6 positive factors, which form 3 factor pairs. Counting negative factors as well doubles that to 12.
What is the prime factorization of 68?
68 = 2² × 17. Its distinct prime factors are 2 and 17.
Is 68 a prime number?
No. 68 is composite because it has 6 factors, more than the two a prime number has.