How Can You Quickly Find the Factors of a Number?

And how can you tell if it’s a prime number?

Factors are numbers that divide exactly into another number without leaving a remainder. No factor can be greater than the number itself.

Quick Method to Find Factors

  1. Begin with 1 and the number itself.
  2. Try dividing the number by 2, 3, etc., up to its square root.
  3. If a number divides exactly, add it and its quotient.
  4. Stop once your trial divisor exceeds the square root.

If the number only has two factors, it is a prime number. If it has more, it is called a composite number.

Step-by-Step: Find Factors of 5

Here’s how to find all the factors of 5:

StepAction
1Start with 1 and 5 → 1, 5
2Try the next whole number: 2
35 ÷ 2 = 2.5 → not a factor
4You’ve reached the square root of 5 (≈2.2), so stop checking further
5No more divisors found. Final list: 1, 5
6Only two factors → 5 is a prime number

Summary

  • Factors of 5: 1, 5
  • Classification: Prime number (only two factors)
  • Highest proper factor: 1

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