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Factor Calculator
Find all the factors, factor pairs, and the prime factorization of a positive integer. Enter any positive whole number up to 1,000,000,000,000 to get instant, accurate results.
Find Factors & Prime Divisors
Results
| Prime Factorization | — |
|---|---|
| Total Count of Factors | — |
| List of Factors | — |
| Factor Pairs | — |
How to find factors of a number
Factors of a number are the numbers that divide it completely without leaving a remainder. To find the factors of a number, follow these methods:
- Trial Division: Start from 1 and test divide the number by integers up to the square root of the number. If a number divides evenly, both the divisor and the resulting quotient are factors. Example: For 12, divide by 1, 2, and 3: 12 ÷ 1 = 12 (factors 1, 12) 12 ÷ 2 = 6 (factors 2, 6) 12 ÷ 3 = 4 (factors 3, 4) Since the square root of 12 is ~3.46, we stop here. The factors of 12 are {1, 2, 3, 4, 6, 12}.
- Factor Pairs: Group the factors into pairs that multiply together to give the original number. For 12, the pairs are (1, 12), (2, 6), and (3, 4).
- Prime Factorization: Break down the number into a product of prime numbers. For 12, this is 2 × 2 × 3 or 2² × 3.
Rules of divisibility
When finding factors manually, divisibility rules can help you quickly check factors:
- Even numbers: Divisible by 2.
- Sum of digits: If the sum of digits is divisible by 3, the number is divisible by 3 (e.g. 12 -> 1+2 = 3).
- Last digit is 0 or 5: Divisible by 5.
- Last digit is 0: Divisible by 10.
Units, rounding, and limits
This calculator works on whole positive numbers only. Decimals, negatives, and zero are rejected. The maximum supported input is 1,000,000,000,000 (1 trillion) to guarantee fast browser processing times without stalling.
FAQ
What is the difference between a factor and a multiple?
Factors are numbers that divide evenly into a number (e.g. factors of 6 are 1, 2, 3, 6). Multiples are numbers that are divisible by that number (e.g. multiples of 6 are 6, 12, 18, 24, etc.).
Is 1 a factor of every number?
Yes, 1 divides every integer evenly, so 1 is a factor of every whole number.
What is a prime number?
A prime number is a positive integer greater than 1 that has exactly two factors: 1 and itself (e.g. 2, 3, 5, 7, 11, etc.). Integers with more than two factors are called composite numbers.