Math Tools
Factor Calculator
Find all factors, factor pairs, and the number of factors of a whole number.
Factor Calculator
Find all factors, factor pairs, and the number of factors of a whole number instantly.
Results
Number of factors
9
Factors
1, 2, 3, 4, 6, 9, 12, 18, 36
Factor pairs
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What this factor calculator does
This calculator finds all positive factors of a whole number and also shows the factor pairs that multiply to make that number.
What is a factor calculator?
A factor calculator is a math tool that finds every whole number that divides another whole number exactly. If a number can divide evenly with no remainder, it is a factor.
This is useful in arithmetic, number theory, prime factorization, simplifying fractions, finding greatest common factors, and checking divisibility. Instead of testing numbers one by one, the calculator shows all factors and factor pairs instantly.
How to find factors of a number
To find the factors of a number, look for every whole number that divides it exactly. For example, to find the factors of 36, test numbers such as 1, 2, 3, 4, 5, 6, and so on. If division leaves no remainder, that number is a factor.
A factor calculator speeds up this process and also groups matching factors into factor pairs. For 36, the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6.
Factors and factor pairs examples
| Number | Factors | Factor pairs | Number of factors |
|---|---|---|---|
| 12 | 1, 2, 3, 4, 6, 12 | 1×12, 2×6, 3×4 | 6 |
| 18 | 1, 2, 3, 6, 9, 18 | 1×18, 2×9, 3×6 | 6 |
| 24 | 1, 2, 3, 4, 6, 8, 12, 24 | 1×24, 2×12, 3×8, 4×6 | 8 |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | 1×36, 2×18, 3×12, 4×9, 6×6 | 9 |
| 49 | 1, 7, 49 | 1×49, 7×7 | 3 |
What are factor pairs?
Factor pairs are two whole numbers that multiply together to produce the original number. For example, the factor pairs of 24 are 1 × 24, 2 × 12, 3 × 8, and 4 × 6.
Factor pairs are especially useful in algebra, rectangle area problems, multiplication tables, and factoring expressions because they show how a number can be built from smaller whole numbers.
Factors vs multiples
Factors and multiples are related, but they are not the same. Factors divide a number exactly, while multiples are the results of multiplying a number by whole numbers.
For example, 3 is a factor of 12 because 12 ÷ 3 = 4 exactly. But 12, 24, and 36 are multiples of 12 because they come from 12 × 1, 12 × 2, and 12 × 3.
Prime numbers and factor count
A prime number has exactly two positive factors: 1 and itself. For example, 13 has only two factors, which are 1 and 13. A composite number has more than two positive factors.
Knowing the number of factors helps when classifying numbers and solving school math problems. This factor calculator also shows the total number of factors for the number you enter.
Where a factor calculator is useful
An online factor calculator is useful for students, teachers, and anyone working with divisibility, fractions, algebra, and basic number theory. It can help check homework, verify answers, and quickly identify factor pairs.
It is also useful in related math topics such as greatest common factor, least common multiple, simplifying ratios, and prime factorization.
Factor calculator FAQ and common factor questions
What is a factor of a number?
A factor is a whole number that divides another whole number exactly with no remainder.
How do you find all factors of a number?
Test which whole numbers divide the number evenly. A factor calculator does this automatically and lists all factors and factor pairs.
What are the factors of 36?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
What are factor pairs?
Factor pairs are pairs of whole numbers that multiply together to make the original number, such as 3 × 12 for 36.
What is the difference between factors and multiples?
Factors divide a number exactly, while multiples are produced by multiplying a number by whole numbers.
Can a prime number have more than two factors?
No. A prime number always has exactly two positive factors: 1 and itself.
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