How to find the factors of 87
Test every whole number from 1 up to the square root of 87 (√87 ≈ 9.327). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 87 ÷ 1 = 87 — so 1 and 87 are factors
- 87 ÷ 2 = 43.5 — not a whole number
- 87 ÷ 3 = 29 — so 3 and 29 are factors
- 87 ÷ 4 = 21.75 — not a whole number
- 87 ÷ 5 = 17.4 — not a whole number
- 87 ÷ 6 = 14.5 — not a whole number
- 87 ÷ 7 = 12.429 — not a whole number
- 87 ÷ 8 = 10.875 — not a whole number
- 87 ÷ 9 = 9.667 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 3, 29 and 87.
Prime factorization of 87
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 87 = 3 × 29. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.
Properties of 87
- 87 is a composite number.
- The sum of all its factors is 120; the sum of its proper factors (excluding 87) is 33, which makes it a deficient number (its proper factors add up to less than itself).
- 87 is not a perfect square, so its factors pair up evenly.
- Multiples of 87 include 174, 261, 348, 435 and so on.
Factors vs. multiples
Factors of 87 are the numbers that divide into it; multiples of 87 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 87?
The factors of 87 are 1, 3, 29 and 87. Each of these divides 87 with no remainder.
How many factors does 87 have?
87 has 4 positive factors, which form 2 factor pairs. Counting negative factors as well doubles that to 8.
What is the prime factorization of 87?
87 = 3 × 29. Its distinct prime factors are 3 and 29.
Is 87 a prime number?
No. 87 is composite because it has 4 factors, more than the two a prime number has.