Every factor of any number.
Enter a whole number to see how many factors it has, all of its factor pairs, whether it is prime or composite, and its special number properties.
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What this means
Factor pairs
| Factor a | Factor b | a × b |
|---|
How factors work
What Are Factors?
Factors are whole numbers that divide evenly into another number with no remainder. The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Every number has at least two factors: 1 and itself. Numbers with exactly two factors are prime numbers.
Finding All Factors
To find all factors, test division from 1 up to the square root of the number. For each divisor that works, you get a factor pair. For 60: 1×60, 2×30, 3×20, 4×15, 5×12, 6×10. Once you pass √60 ≈ 7.7, you have found all pairs.
Factor Pairs
A factor pair is two numbers that multiply to give the original number. For 60, the factor pairs are (1,60), (2,30), (3,20), (4,15), (5,12), (6,10). Perfect squares have an odd number of factors because one pair has the same number twice (e.g., 36: 6×6).
Factors in Mathematics
Factoring is fundamental to simplifying fractions, finding GCF and LCM, solving equations, and number theory. In algebra, factoring polynomials uses similar concepts. Understanding the factors of a number reveals its divisibility properties and its relationship to other numbers.
Common questions
How many factors does a number have?
It depends on the number. Prime numbers have exactly 2 factors. Highly composite numbers like 60 have many. To count factors from prime factorization, add 1 to each exponent and multiply: 60 = 2² × 3 × 5 → (2+1)(1+1)(1+1) = 12 factors.
What is the difference between factors and multiples?
Factors divide INTO the number (going smaller). Multiples are the number multiplied BY integers (going larger). 3 is a factor of 12. 12, 24, 36 are multiples of 12.
Does every number have an even number of factors?
No. Perfect squares have an odd number of factors because the square root is counted once instead of twice. For example, 36 has factors: 1,2,3,4,6,9,12,18,36, that is 9 factors (odd).
What is prime factorization?
Prime factorization breaks a number into a product of prime numbers. For example, 60 = 2² × 3 × 5. Every composite number has a unique prime factorization (Fundamental Theorem of Arithmetic).
For education and reference. Very large numbers may take a moment to factor in your browser.