The Factoring Calculator finds the set of factors or divisors of a positive integer. Enter a positive number to find its factors.
The factors of a number include all numbers that divide evenly into that number. Consider the number 10. Since 10 ÷ 2 = 5, you can conclude that both 2 and 5 are factors of 10.
You can also think about factors in terms of multiplication: when you multiply two integer numbers together, the result is another integer. You can say that the original two numbers are factors of the third. So factors are numbers that are multiplied together to get another number.
How to Factor Numbers: Factorization
This calculator factors numbers by trial division. If you'd like to use trial division to find the factors of a number, follow these steps.
- Find the square root of the integer number n and round up to the next whole number. Let's call this number s.
- Start with the number "1" and find the corresponding factor pair: n ÷ 1 = n. So 1 and n are a factor pair because division results in a whole number with zero remainder.
- Do the same with the number "2" and proceed testing all integers through the rounded-up square root s (n ÷ 2, n ÷ 3, n ÷ 4... n ÷ s). Record the factor pairs where division results in whole integer numbers with zero remainders.
- Once you have recorded all factor pairs you have successfully factored the number n.
Factors of 18:
- The square root of 18 is 4.2426, rounded up to the next whole number is 5
- Testing the integer values 1 through 5 for division into 18 we get these factor pairs: (1 and 18), (2 and 9), (3 and 6). The factors of 18 are 1, 2, 3, 6, 9, 18.
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