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what is common factor

A common factor is a number that divides two or more numbers exactly, with no remainder.

Put simply:
If a number “goes into” two (or more) numbers evenly, it’s a common factor of those numbers.

What is a factor?

  • A factor of a number is a whole number that divides it exactly.
  • Example: Factors of 12 are 1, 2, 3, 4, 6, 12 (each divides 12 with remainder 0).

So factors are like the “building blocks” you can multiply to get the original number.

What is a common factor?

When two or more numbers share the same factor, that shared number is a common factor.

Example 1: 12 and 18

  • Factors of 12: 1, 2, 3, 4, 6, 12
  • Factors of 18: 1, 2, 3, 6, 9, 18

Common factors (in both lists): 1, 2, 3, 6.

These are the numbers that divide both 12 and 18 exactly.

Greatest common factor (GCF)

Often we care about the greatest common factor (GCF) , also called highest common factor (HCF).

  • From the example above, common factors of 12 and 18 are 1, 2, 3, 6.
  • The largest of these is 6, so the GCF of 12 and 18 is 6.

GCF is very useful for simplifying fractions and breaking expressions into simpler parts.

How to find common factors (quick steps)

  1. List factors of each number.
  2. Circle or note the factors that appear in every list.
  3. Those shared numbers are the common factors.

Example 2: 6 and 9

  • Factors of 6: 1, 2, 3, 6
  • Factors of 9: 1, 3, 9

Common factors: 1, 3.

One more way to think about it

You can think of a common factor as a “shared divisor” or a shared piece that fits evenly into different numbers.

For example, if two friends each bring chocolates in packs of 12 and 18, any number of chocolates they can group equally from both packs (like groups of 6) is tied to a common factor of 12 and 18.

Mini FAQ

  • Is 1 always a common factor?
    Yes, 1 divides every whole number, so it’s always a common factor.
  • What if the only common factor is 1?
    Then the numbers are called co-prime (or relatively prime).

TL;DR:
A common factor is a number that can divide each of two or more numbers exactly, and the greatest common factor is the biggest such shared number.

Information gathered from public forums or data available on the internet and portrayed here.