Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Find every pair of factors that multiply together to give a target number.
Whole numbers from 1 to 1,000,000.
Enter a whole number to see its factor pairs.
This tool finds every pair of whole numbers that multiply together to equal your target number, by trial division up to the square root of the target.
Enter a whole number from 1 to 1,000,000 (larger numbers return no result). Every factor pair appears instantly, listed from smallest to largest.
The finder accepts whole numbers from 1 up to 1,000,000. Anything outside that range, including zero, gives no pairs. Decimal input is rounded to the nearest whole number and negative input is converted to its absolute value. Each pair is displayed as a × b with a always the smaller factor, so the list runs from 1 × n up to the pair closest together. The tool only tests divisors up to the square root of your number, then derives the partner factor by division, so it never lists the same pair twice in reverse order.
Take 72. The square root is about 8.49, so the tool tests 1 through 8. The numbers that divide evenly are 1, 2, 3, 4, 6 and 8, which produce these pairs:
That gives six pairs and twelve distinct factors in total (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72). Each pair counts two factors, unless the number is a perfect square.
When a number is a perfect square, the last pair repeats a single value. For 36 the final pair is 6 × 6, which counts as one factor, not two. That is why perfect squares always have an odd number of factors while every other number has an even number. Spotting a pair with equal parts is a quick way to confirm a number is a perfect square.
If the tool returns only 1 × n, the number has no other divisors and is prime. The number 1 itself returns the single pair 1 × 1. A long list of pairs signals a highly composite number, which is convenient when you need flexible divisibility, such as choosing a length that can be cut into many equal segments.
A reliable way to verify the list is to multiply each pair back together and confirm it equals your target. Then check that no whole number below the square root was skipped. For a quick estimate of how many pairs to expect, remember that numbers with several small prime factors, such as 60, 72 or 120, have many pairs, while numbers built from one prime raised to a power, such as 64, have few. If a number you expected to be divisible by something is missing that divisor, re-check the entry for a typo.
Yes -- a prime number will show exactly one factor pair: 1 and itself.
1,000,000. Values above that, or below 1, produce no pairs.
36 is a perfect square, so its middle factor pairs with itself. This is the only case where a pair has two identical numbers.
No. Only positive pairs are listed. Every positive pair also has a negative twin, such as -6 × -12 for 72.
Double the number of pairs, and subtract one if the last pair has two equal numbers.
Reference: NIST Weights and Measures