How to use the factor calculator
Type any whole number from 1 to 1,000,000,000,000. The calculator lists every factor in order, groups them into the pairs that multiply to your number, writes the prime factorization with exponents, adds up the factors and tells you whether the number is prime or a perfect square. The note under the results shows the exponent formula that counts the factors without listing them.
Factors versus multiples
A factor (or divisor) of a number divides it exactly, with no remainder: 8 is a factor of 360 because 360 ÷ 8 = 45. A multiple goes the other way: 720 is a multiple of 360 because 360 × 2 = 720. Factors are never larger than the number; multiples are never smaller. The LCM calculator works with multiples and the GCF calculator with shared factors.
Factor pairs
Factors come in pairs whose product is the number: for 360 they are 1 × 360, 2 × 180, 3 × 120, 4 × 90, 5 × 72, 6 × 60, 8 × 45, 9 × 40, 10 × 36, 12 × 30, 15 × 24 and 18 × 20 — 12 pairs, so 24 factors in all. You only need to test divisors up to the square root (√360 ≈ 18.97): every factor above it is the partner of one below it.
Prime factorization with a factor tree
Split the number into any two factors, then keep splitting until every branch ends in a prime: 360 = 36 × 10; 36 = 6 × 6 and 10 = 2 × 5; 6 = 2 × 3. Collect the leaves: 2, 2, 2, 3, 3, 5, or 2³ × 3² × 5. Every whole number greater than 1 has exactly one prime factorization, however you draw the tree.
The factorization also counts the factors: add 1 to each exponent and multiply, (3 + 1) × (2 + 1) × (1 + 1) = 24, because a factor picks 0–3 twos, 0–2 threes and 0–1 fives. The sum of the factors is (1 + 2 + 4 + 8) × (1 + 3 + 9) × (1 + 5) = 15 × 13 × 6 = 1,170.
Divisibility rules
| Divisible by | Rule | 360? |
|---|---|---|
| 2 | Last digit is even | Yes (0) |
| 3 | Digit sum divisible by 3 | Yes (3 + 6 + 0 = 9) |
| 4 | Last two digits divisible by 4 | Yes (60 = 4 × 15) |
| 5 | Ends in 0 or 5 | Yes |
| 6 | Divisible by both 2 and 3 | Yes |
| 8 | Last three digits divisible by 8 | Yes (360 = 8 × 45) |
| 9 | Digit sum divisible by 9 | Yes (9) |
| 10 | Ends in 0 | Yes |
360 passes all eight, which is why it is such a convenient number for degrees in a circle: it splits evenly into halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfths.
Primes, composites and perfect squares
A prime has exactly two factors, 1 and itself. To test 97, try the primes up to √97 ≈ 9.8 — 2, 3, 5 and 7 — and none divides it, so 97 is prime. A composite number has more than two factors. The number 1 has only one factor and is neither prime nor composite. A perfect square like 144 = 12² has an odd number of factors (15 for 144), because the middle pair 12 × 12 counts once.
The row "sum of proper factors" adds every factor except the number itself and names the result: 28 is perfect (1 + 2 + 4 + 7 + 14 = 28), 12 is abundant (its proper factors sum to 16) and every prime is deficient (its only proper factor is 1).
Frequently asked questions
What are the factors of 360?
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360 — 24 factors in 12 pairs. Its prime factorization is 2³ × 3² × 5.
Is 1 a prime number?
No. A prime needs exactly two different factors, 1 and itself, and 1 has only one. Treating 1 as prime would also break the rule that every number has a single prime factorization.
How can I tell whether a large number is prime?
Divide by every prime up to its square root; if none divides it, it is prime. For 1,000,000,007 that means testing primes up to 31,623 — a few thousand divisions, which the calculator does instantly.
What is the difference between factors and prime factors?
Factors are all the numbers that divide evenly: 360 has 24 of them. Prime factors are only the primes among them — 2, 3 and 5 — and the prime factorization 2³ × 3² × 5 records how many times each one is used.
How many factors does a number have without listing them?
Write its prime factorization, add 1 to each exponent and multiply. 2³ × 3² × 5 gives (3 + 1)(2 + 1)(1 + 1) = 24. A prime p has 2 factors, and p² has 3.
Last updated: October 9, 2026