Factor Calculator
Enter any whole number below to instantly find every factor, factor pair, and its prime factorization.
Factor pairs of 30
Every factor has a partner that multiplies with it to give 30. Listing pairs from the outside in is the fastest way to find all the factors: once the two numbers in a pair meet in the middle, you have them all.
| Pair | Check |
|---|---|
| 1 and 30 | 1 × 30 = 30 |
| 2 and 15 | 2 × 15 = 30 |
| 3 and 10 | 3 × 10 = 30 |
| 5 and 6 | 5 × 6 = 30 |
Prime factorization of 30, step by step
Divide by the smallest prime that goes in evenly, then repeat on the result until you reach 1. The divisors you used are the prime factors.
| Step | Divide | Result |
|---|---|---|
| 1 | 30 ÷ 2 | 15 |
| 2 | 15 ÷ 3 | 5 |
| 3 | 5 ÷ 5 | 1 |
So 30 = 2 × 3 × 5, written compactly as 2 × 3 × 5.
Divisibility checks for 30
The quick rules a student uses before dividing, applied to 30:
| Divisible by | Rule | For 30 | Result |
|---|---|---|---|
| 2 | last digit is even | last digit 0 | yes |
| 3 | digit sum divisible by 3 | digits add to 3 | yes |
| 4 | last two digits divisible by 4 | 30 ÷ 4 | no |
| 5 | last digit is 0 or 5 | last digit 0 | yes |
| 6 | divisible by both 2 and 3 | even, digit sum 3 | yes |
| 8 | last three digits divisible by 8 | 30 ÷ 8 | no |
| 9 | digit sum divisible by 9 | digits add to 3 | no |
| 10 | last digit is 0 | last digit 0 | yes |
What Are Factors?
A factor of a number is a whole number that divides into it evenly, with nothing left over. Every number has at least two factors — 1 and itself — and most numbers have several more. Factors are the building blocks behind fraction simplification, GCF, LCM, and prime factorization.
How to Find All Factors of a Number, Step by Step
- Start with 1 and the number itself — these are always factors.
- Test each whole number from 2 up to the square root of the number. If it divides evenly, both it and the paired result are factors.
- Collect every factor found and sort them from smallest to largest.
Worked example
Find all factors of 36.
1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 — the square root of 36 is exactly 6, so the search stops there.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Prime factorization: 36 = 2^2 × 3^2
Factors of Popular Numbers
Browse All Numbers
Every one of these links to its own page with the full factor list, factor pairs, and prime factorization already worked out.
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Keep going
- Want the answer for a specific number without running the calculator? Every factor list from 1 to 100 is laid out in one table. Factors of every number
- A number's factor list is the raw material for GCF; the GCF calculator compares two lists to find the largest one they share. GCF Calculator
- A number's prime factorization also shows instantly whether it's a perfect square; the square root calculator uses that to simplify the radical. Square Root Calculator
Frequently Asked Questions
What is a factor of a number?
A factor of a number is a whole number that divides into it evenly, with no remainder. For example, 5 is a factor of 30 because 30 ÷ 5 = 6 exactly.
How do you find all the factors of a number?
Test each whole number from 1 up to the square root of the number. Whenever one divides evenly, both it and the paired result (the number divided by it) are factors. This is faster than checking every number up to the target itself, since factors always come in pairs.
What's the difference between a factor and a multiple?
A factor divides evenly into a number (factors of 12 include 1, 2, 3, 4, 6, 12). A multiple is what you get by multiplying a number by a whole number (multiples of 12 include 12, 24, 36, 48...). They're opposite directions of the same relationship.
What is prime factorization?
Prime factorization breaks a number down into the prime numbers that multiply together to make it — for example, 30 = 2 × 3 × 5. Every whole number greater than 1 has exactly one prime factorization (this is called the Fundamental Theorem of Arithmetic).
How many factors does a prime number have?
Exactly two: 1 and itself. That's the definition of a prime number. A composite number always has more than two factors.
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