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How to Find Factors of a Number




Finding the factors of a number involves identifying all the whole numbers that divide that number evenly, without leaving a remainder. Factors are fundamental in number theory and are used in various areas of mathematics, including algebra and arithmetic.

Steps to Find Factors

  1. Start with the number you want to find factors for. Let’s call this number ‘N’.
  2. Begin with the smallest whole number, which is 1. Check if it divides N without leaving a remainder. If it does, it is a factor of N.
  3. Continue checking each successive whole number (2, 3, 4, …) to see if it divides N evenly.
  4. Stop when you reach a number that is more than half of N, as factors of a number are always less than or equal to half of that number, except for the number itself.
  5. Include N itself as a factor, as every number is divisible by itself.

Example 1: Finding Factors of 12

Let’s find the factors of 12. Check each number from 1 to 6 (half of 12):

1 divides 12 (12 ÷ 1 = 12), so 1 is a factor. Similarly, 2, 3, 4, and 6 divide 12 evenly. Therefore, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Example 2: Finding Factors of 17

Let’s find the factors of 17. Check each number from 1 to 8 (half of 17):

Only 1 and 17 divide 17 evenly without a remainder. Therefore, the factors of 17 are 1 and 17, making it a prime number.

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