How to find the factors of 58
Test every whole number from 1 up to the square root of 58 (√58 ≈ 7.616). Each number that divides evenly gives you two factors at once: the divisor and the quotient.
- 58 ÷ 1 = 58 — so 1 and 58 are factors
- 58 ÷ 2 = 29 — so 2 and 29 are factors
- 58 ÷ 3 = 19.333 — not a whole number
- 58 ÷ 4 = 14.5 — not a whole number
- 58 ÷ 5 = 11.6 — not a whole number
- 58 ÷ 6 = 9.667 — not a whole number
- 58 ÷ 7 = 8.286 — not a whole number
Collecting both numbers from every successful division gives the complete list: 1, 2, 29 and 58.
Prime factorization of 58
Divide by the smallest prime that fits, and keep going until the quotient is 1:
The primes you divided by give 58 = 2 × 29. From the exponents you can also count the factors without listing them: (1 + 1) × (1 + 1) = 4.
Properties of 58
- 58 is a composite number.
- The sum of all its factors is 90; the sum of its proper factors (excluding 58) is 32, which makes it a deficient number (its proper factors add up to less than itself).
- 58 is not a perfect square, so its factors pair up evenly.
- Multiples of 58 include 116, 174, 232, 290 and so on.
Factors vs. multiples
Factors of 58 are the numbers that divide into it; multiples of 58 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 58?
The factors of 58 are 1, 2, 29 and 58. Each of these divides 58 with no remainder.
How many factors does 58 have?
58 has 4 positive factors, which form 2 factor pairs. Counting negative factors as well doubles that to 8.
What is the prime factorization of 58?
58 = 2 × 29. Its distinct prime factors are 2 and 29.
Is 58 a prime number?
No. 58 is composite because it has 4 factors, more than the two a prime number has.