Find all factors and the prime factorization of any whole number.
Every integer from 1 up to the square root of your number is tested for divisibility; each divisor found pairs with a matching co-factor (for example, if 4 divides 12, then 12÷4=3 is also a factor). The prime factorization is found separately by dividing out the smallest prime repeatedly until only primes remain.
The factors of a number are every whole number that divides it evenly. The prime factorization is the unique set of prime numbers that multiply together to produce it — every whole number greater than 1 has exactly one prime factorization (the Fundamental Theorem of Arithmetic).
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 (12 factors total). Prime factorization: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
Once you have the prime factorization, the total factor count follows directly: add 1 to each prime's exponent, then multiply those results together. For 60 = 2² × 3¹ × 5¹, that's (2+1) × (1+1) × (1+1) = 3 × 2 × 2 = 12 factors — which matches the 12 factors listed above. Numbers with more repeated prime factors (like 2&sup6;=64) tend to have more total factors than numbers of similar size built from fewer, larger primes.
Beyond classroom math, factoring underlies how computers check for shared divisors, reduce fractions in software, and — for very large numbers — the difficulty of factoring is the basis of RSA encryption, one of the most widely used methods for securing online communication. Small numbers like the ones this tool handles factor instantly; numbers hundreds of digits long can take even powerful computers an impractical amount of time, which is exactly why that difficulty is useful for cryptography.
What is a factor? A factor of a number is any whole number that divides it exactly, with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
What is prime factorization? Prime factorization breaks a number down into the prime numbers that multiply together to produce it — for example, 12 = 2 × 2 × 3.
How is this different from the LCM & GCF calculator? This tool lists every factor of one number; the LCM & GCF calculator compares two or more numbers to find their least common multiple and greatest common factor.
What does it mean if a number has only two factors? It means the number is prime — its only factors are 1 and itself.
Is 1 a prime number? No. By definition, a prime number has exactly two distinct factors (1 and itself); 1 only has one factor (itself), so it's classified separately as a "unit," not a prime.
Is 1 a factor of every number? Yes — 1 divides every whole number evenly, so it's always the smallest factor in the list, just as the number itself is always the largest.
| Divisor | Test |
|---|---|
| 2 | The last digit is even. |
| 3 | The sum of the digits is divisible by 3. |
| 4 | The last two digits form a number divisible by 4. |
| 5 | The number ends in 0 or 5. |
| 6 | It passes both the 2 and 3 tests. |
| 9 | The sum of the digits is divisible by 9. |
| 10 | The number ends in 0. |
You only need to test divisors up to the square root of the number, because every factor below it pairs with one above it. To list the factors of 36, test 1 through 6 and record each pair: 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 with itself.
Perfect squares such as 16, 25 and 36 have an odd number of factors because one factor pairs with itself. For example, 36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36.
How can I tell quickly if a number is divisible by 3? Add its digits. If the sum is divisible by 3, so is the number. For 417 the sum is 12, so 417 is divisible by 3.
Is there a limit to the size of the number? Very large numbers take longer to factor and may be limited by what your browser can calculate quickly.