Math · Number theory
Factors of a number calculator.
List every factor of a whole number, its factor pairs, how many factors it has, whether it is prime, and its prime factorization.
Inputs
Factors
Enter a whole number.
What are factors?
Factors are the numbers you multiply together to get another number. They come in pairs: 2 × 6 = 12 and 3 × 4 = 12, and of course 1 × 12 = 12, so the factors of 12 are 1, 2, 3, 4, 6, 12.
The outside-in method. Start at 1 and pair it with the number itself, then try 2, 3, 4 and so on, putting each exact divisor and its partner at the two ends of the list. You can stop when the numbers meet in the middle. For 20: 1 × 20, 2 × 10 and 4 × 5, so the factors are 1, 2, 4, 5, 10, 20.
Prime and composite. A prime number has exactly two factors, 1 and itself: 97 has only 1 and 97, so it is prime. A number with more factors is composite. 360 has 24 factors and its prime factorization is 2^3 × 3^2 × 5.
This list shows positive factors. Every factor also has a negative partner (for example -2 × -6 = 12), and factors are normally whole numbers, not fractions.
Frequently asked questions
What are the factors of 12?
1, 2, 3, 4, 6, 12. The pairs are 1 × 12, 2 × 6 and 3 × 4.
How do you find all the factors of a number?
Test each whole number from 1 up to the square root. Every exact divisor gives a pair. For 20 the pairs are 1 × 20, 2 × 10 and 4 × 5, giving 1, 2, 4, 5, 10, 20.
How do I tell if a number is prime?
A prime has exactly two factors, 1 and itself. 97 has only 1 and 97, so it is prime. The number 1 has just one factor.
How many factors does 360 have?
24. Its prime factorization is 2^3 × 3^2 × 5.
Are negative numbers factors too?
Yes, since two negatives multiply to a positive, but factors are usually listed as positive whole numbers.
Sources
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For learning
For the GCF and LCM of two numbers, with prime factorization, see the GCF and LCM calculator. Results are rounded for display. Check with your teacher's required method when you hand in homework.