How to Find All The Factors of a Number Quickly and Easily

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Finding the factors of a number is an important math skill for basic arithmetic, algebra and calculus. The factors of a number are any numbers that divide into it exactly, including 1 and the number itself. In other words, every number is the product of multiple factors.

TL;DR (Too Long; Didn't Read)

The quickest way to find the factors of a number is to divide it by the smallest prime number (bigger than 1) that goes into it evenly with no remainder. Continue this process with each number you get, until you reach 1.

Prime Numbers

A number that can only be divided by 1 and itself is called a prime number. Examples of prime numbers are 2, 3, 5, 7, 11 and 13. The number 1 is not considered a prime number because 1 goes into everything.

Divisibility Rules

Some divisibility rules can help you find the factors of a number. If a number is even, it's divisible by 2, i.e. 2 is a factor. If a number's digits total a number that's divisible by 3, the number itself is divisible by 3, i.e. 3 is a factor. If a number ends with a 0 or a 5, it's divisible by 5, i.e. 5 is a factor.

If a number is divisible twice by 2, it's divisible by 4, i.e. 4 is a factor. If a number is divisible by 2 and by 3, it's divisible by 6, i.e. 6 is a factor. If a number is divisible twice by 3 (or if the sum of the digits is divisible by 9), then it's divisible by 9, i.e. 9 is a factor.

Finding Factors Quickly

Establish the number you want to find the factors of, for example 24. Find two more numbers that multiply to make 24. In this case, 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 = 24. This means the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Factor negative numbers in the same way as positive numbers, but make sure the factors multiply together to produce a negative number. For example, the factors of -30 are -1, 1, -2, 2, -3, 3, -5, 5, -6, 6, -10, 10, -15 and 15.

If you have a large number, it's more difficult to do the mental math to find its factors. To make it easier, create a table with two columns and write the number above it. Using the number 3784 as an example, start by dividing it by the smallest prime factor (bigger than 1) that goes into it evenly with no remainder. In this case, 2 x 1892 = 3784. Write the prime factor (2) in the left column and the other number (1892) in the right column.

Continue with this process, i.e. 2 x 946 = 1892, adding both numbers to the table. When you reach an odd number (e.g., 2 x 473 = 946), divide by small prime numbers besides 2 until you find one that divides evenly with no remainder. In this case, 11 x 43 = 473. Continue the process until you reach 1.

References

About the Author

Claire is a writer and editor with 18 years' experience. She writes about science and health for a range of digital publications, including Reader's Digest, HealthCentral, Vice and Zocdoc.

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