Find all factors, prime factors and factor pairs of any number — with prime factorisation in index notation and a complete factor pair list.
Enter your figures and click Calculate to see your results.
Enter any positive whole number — the calculator lists every factor, shows prime factorisation and all factor pairs.
Press the Calculate button. All results appear instantly — no page reload, no waiting.
Results appear in the panel on the right with all key values clearly labelled. Use Copy to grab the result or Download to save a text file.
A factor of a number is a whole number that divides into it exactly with no remainder. For 12: factors are 1, 2, 3, 4, 6 and 12. Every integer has at least two factors (1 and itself). Numbers with exactly two factors are prime numbers; all others are composite.
Prime factorisation expresses a number as a product of prime numbers only. For 360: 360 = 2³ × 3² × 5. The Fundamental Theorem of Arithmetic states that every integer greater than 1 has exactly one unique prime factorisation. It is the basis of many areas of number theory and cryptography.
Only test divisors up to the square root of the number. If n is divisible by d, then n÷d is also a factor, so you automatically find both factors at once. For example, to factor 100: test up to √100 = 10. You only need to check 2, 3, 4, 5, 6, 7, 8, 9, 10 rather than all 100 numbers.
A perfect number equals the sum of all its proper factors (factors excluding itself). The smallest perfect number is 6 (1+2+3=6). The next is 28 (1+2+4+7+14=28). Only 51 perfect numbers are known, all are even, and whether any odd perfect number exists is one of the oldest unsolved problems in mathematics.
They are inverse concepts: if 3 is a factor of 12, then 12 is a multiple of 3. Factors divide into a number exactly; multiples are numbers you get by multiplying. Every number has a finite number of factors but infinitely many multiples. The factors of 12 are {1,2,3,4,6,12}; the multiples of 12 are {12,24,36,48,...}.
