What is the GCF of 180, 108, and 75?

il2k3s2u7

il2k3s2u7

Answered question

2022-05-19

What is the GCF of 180, 108, and 75?

Answer & Explanation

Ada Harrington

Ada Harrington

Beginner2022-05-20Added 12 answers

Step 1
In most cases we should be able to find the GCF fairly easily by just knowing the multiplication tables up to 12 × 12 . Sometimes a bigger number might be included which we do not know well. This is just such a case.
Using factor trees mentally will allow you write all the ' factors.
(for example: 108 = 12 × 9 = ( 4 × 3 ) × ( 3 × 3 ) = 2 × 2 × 3 × 3 × 3 )
It is good to have a method available for cases when we cannot find the GCF by inspection.
In order to find the GCF (and the LCM) write each number as the product of its ' factors.
180 = 2 × 2 × 3 × 3 × 5
× × 108 = 2 × 2 × 3 × 3 × 3
75 = 3 × 5 × 5
G C F = 3
From this it is very clear that the only common factor is 3.
(I find this result surprising - I would thought it would be higher.)
If we needed the LCM it can be calculated easily from this format:
Include each column of factors, do not count factors that are in the same column twice.
L C M = 2 × 2 × 3 × 3 × 3 × 5 × 5 = 2 2 × 3 3 × 5 2 = 2700
Brooke Webb

Brooke Webb

Beginner2022-05-21Added 1 answers

Step 1
Factors of 180 are { 1 , 2 , 3 , 4 , 5 , 6 , 9 , 10 , 12 , 15 , 18 , 20 , 30 , 36 , 45 , 60 , 90 , 180 }
Factors of 108 are { 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 108 }
Factors of 75 are { 1 , 3 , 5 , 15 , 25 , 75 }
Common factors are just { 1 , 3 } and
Greatest Common Factor is 3.

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