Module 3 · Factors and multiples · Lesson 12 of 39

Greatest common factor (GCF)

The largest number that divides into both numbers.

In this lesson · about 10 minutes

  • Find the GCF with prime factorizations
  • Check a GCF

A common factor divides evenly into both numbers. The greatest common factor (GCF), also called the greatest common divisor (GCD), is the largest one.

To find it, factor both numbers into primes and keep only the primes they share, as many times as they appear in both.

Worked example

GCF of 14 and 28

Break each number into primes.

    Step 0 of 4

    Try it · interactive

    Multiples and factors side by side

    The biggest number on both factor lists is the GCF.

    Multiples (for the LCM)

    6:6121824303642485460
    8:8162432404856647280

    Factors (for the GCF)

    6:1236
    8:1248

    LCM = 24, the first number on both multiple lists. By primes: 2 · 3 and 2³.

    GCF = 2, the biggest number on both factor lists.

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    Question 1

    1.Which is bigger for 6 and 8?

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