How do you use a factor tree to find the greatest common factor?

Answer 1

Factor trees are used to determine the prime factors of a number. When you have the prime factors of each of the numbers you are comparing, find out which prime factors they have in common. When you have the prime factors that they all have in common, multiply those prime factors together. This number will be the greatest common factor.

Example: Find the greatest common factor of 18 and 54.

18

3 x 6

3 x (2x3)

The prime factors of 18 are 2, 3, and 3.

54

6 x 9

(2x3) x (3x3)

The prime factors of 54 are 2, 3, 3, and 3.

The prime factors that 18 and 54 have in common are 2, 3 and 3, so the greatest common factor is 2 x 3 x 3 = 18.

Example: Find the greatest common factor of 24 and 52.

24

4 x 6

(2x2) x (2x3)

The prime factors of 24 are 2, 2, 2, and 3.

52

2 x 26

2 x (2x13)

The prime factors of 52 are 2, 2, and 13.

The prime factors that 24 and 52 have in common are 2 and 2, so the greatest common factor is 2 x 2 = 4.

Make a factor tree for the first number and when you are finished reducing the number to its prime factors, put them in order. Then, do the same with the other number. Put the two lists of prime factors in two rows, so you can compare them, like this: 12 = 2 x 2 x 3

8= 2 x 2 x 2 After that, line them up to determine which ones match. They both have two 2s, but nothing else is the same, so multiply both together

2 x 2 = 4

to get the greatest common factor.

4 is the Greatest Common Factor (GCF) Hope it helps, Sakura They don't have to align vertically. E.g.:

6 = 2 x 3

15= 3 x 5

GCF=3 (since each of the numbers has a factor of 3).

Basically, for each Prime number p, you check how many times p appears in each of the two numbers, and then take the minimum. In this case: 2 occurs 1 time in 6 and 0 times in 15; the minimum of 1 and 0 is 0; therefore 2 occurs 0 times in the GCF. You do this for each of the primes, and get 3.