Factors and Multiples

GCD by Listing

Find the greatest common divisor of 24 and 36 by listing all factors of each number, identifying the shared ones, and picking the largest. GCD(24, 36) = 12.

greatest-common-divisor The GCD of two numbers is the largest factor they share. List every factor of each number, then circle the ones that appear on both lists. The biggest circled number is the GCD. It tells you the largest piece both numbers can be evenly divided into.

Example

Find the greatest common factor of 24 and 36 by listing factors.

highlighted = computed this step

Step 1 — Set up

Set up the numbers to test.

gcd⁡(24,36)\gcd( 24 , 36 )
List factors of 24 and 36, then look for matches.factors of 24not listed yetfactors of 36not listed yetcommonwait for both listsgreatest common factor--

Step 2 — List first factors

List every factor of 24.

factors of 24:1,2,3,4,6,8,12,24\mathrm{factors\ of}\ 24 : \hl{1}, \hl{2}, \hl{3}, \hl{4}, \hl{6}, \hl{8}, \hl{12}, \hl{24}
First list every factor of 24.factors of 241234681224factors of 36not listed yetcommonwait for both listsgreatest common factor--

Step 3 — List second factors

List every factor of 36.

factors of 36:1,2,3,4,6,9,12,18,36\mathrm{factors\ of}\ 36 : \hl{1}, \hl{2}, \hl{3}, \hl{4}, \hl{6}, \hl{9}, \hl{12}, \hl{18}, \hl{36}
Now list every factor of 36.factors of 241234681224factors of 36123469121836commonwait for both listsgreatest common factor--

Step 4 — Mark common factors

Mark the 6 common factors.

common: 1,2,3,4,6,12\mathrm{common:}\ \hl{1}, \hl{2}, \hl{3}, \hl{4}, \hl{6}, \hl{12}
Mark the 6 common factors.factors of 241234681224factors of 36123469121836common1234612greatest common factor--

Step 5 — Result

The greatest common factor is 12.

gcd⁡(24,36)=12\gcd( 24 , 36 )= \hl{12}
The greatest common factor is 12.factors of 241234681224factors of 36123469121836common1234612greatest common factor12