How Can You Quickly Find the Factors of a Number?

And what if a number only has 1 and itself as factors?

Factors are numbers that divide exactly into another number without leaving a remainder. They are always less than or equal to the original number.

Quick Method to Find Factors

  1. Start with 1 and the number itself.
  2. Try dividing the number by 2, 3, and so on up to its square root.
  3. If a number divides in evenly, add both the divisor and quotient to your list.
  4. Stop once you’ve exceeded the square root of the number.

If the final list has only two values — 1 and the number itself — then the number is a prime.

Step-by-Step: Find Factors of 7

Here’s how to find all the factors of 7:

StepAction
1Start with 1 and 7 → 1, 7
2Try dividing 7 by 2 → 7 ÷ 2 = 3.5 → Not a factor
3Stop at $\sqrt{7}$ (≈2.6), since no further exact divisors exist
4Final factor list: 1, 7
5Only two factors found → 7 is a prime number

Summary

  • Factors of 7: 1 and 7
  • Classification: Prime number (only two factors)
  • Highest proper factor: 1

Now try another one: