# What is the greatest common factor of 54 and 36?

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Apr 5, 2016

It is $18$

#### Explanation:

Because

$3 \cdot 18 = 54$
$2 \cdot 18 = 36$

Also

The factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 -1, -2, -3, -6, -9, -18, -27, -54

The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 -1, -2, -3, -4, -6, -9, -12, -18, -36

The greatest common factor of 54 and 36 = 18

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Jul 15, 2017

$H C F = 18$

#### Explanation:

When working with HCF and/or LCM, write each number as the product of its prime factors. That will tell you everything you need to know about a number.

Look for all the common factors:

$\text{ } 36 = 2 \times 2 \times 3 \times 3$
" "ul(54 = 2" "xx3xx3xx3)
$H C F = 2 \text{ "xx3xx3" } = 18$

The highest common factor is the product of all the common factors.

This is a very quick and effective method, especially if you are working with large numbers where you might not know all of the factors.

The product of the prime factors will tell you whether a number is a power, like a square or a cube.
You can also use the prime factors to determine all the other factors as well.

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EET-AP Share
Oct 9, 2017

The greatest common factor of $54 \mathmr{and} 36$ is $18$.

#### Explanation:

What is the greatest common factor (GCF)?
That is the largest number that will divide into all those given.
To find it, the smallest prime numbers should be divided into each one. Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19.

For the given numbers $54$ and $36$, both can be divided by $2$ to get $27$ and $18$.

$27$ will not divide into both, but $18$ will, so it is the GCF.

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