How to find the factors of 77
Test every whole number from 1 up to the square root of 77 (√77 ≈ 8.775). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 77 ÷ 1 = 77 — so 1 and 77 are factors
- 77 ÷ 2 = 38.5 — not a whole number
- 77 ÷ 3 = 25.667 — not a whole number
- 77 ÷ 4 = 19.25 — not a whole number
- 77 ÷ 5 = 15.4 — not a whole number
- 77 ÷ 6 = 12.833 — not a whole number
- 77 ÷ 7 = 11 — so 7 and 11 are factors
- 77 ÷ 8 = 9.625 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 7, 11 and 77.
Prime factorization of 77
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 77 = 7 × 11. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.
Properties of 77
- 77 is a composite number.
- The sum of all its factors is 96; the sum of its proper factors (excluding 77) is 19, which makes it a deficient number (its proper factors add up to less than itself).
- 77 is not a perfect square, so its factors pair up evenly.
- Multiples of 77 include 154, 231, 308, 385 and so on.
Factors vs. multiples
Factors of 77 are the numbers that divide into it; multiples of 77 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 77?
The factors of 77 are 1, 7, 11 and 77. Each of these divides 77 with no remainder.
How many factors does 77 have?
77 has 4 positive factors, which form 2 factor pairs. Counting negative factors as well doubles that to 8.
What is the prime factorization of 77?
77 = 7 × 11. Its distinct prime factors are 7 and 11.
Is 77 a prime number?
No. 77 is composite because it has 4 factors, more than the two a prime number has.