What is the GCF of 36 and 60?

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What is the GCF of 36 and 60?

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Answer 1 · 2016-03-31T03:57:22

Greatest Common Factor is $12$ $12$ .

Explanation:

Factors of $36$ $36$ are ${1, 2, 3, 4, 6, 9, 12, 18, 36}$ ${1,2,3,4,6,9,12,18,36}$ .

Factors of $60$ $60$ are ${1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}$ ${1,2,3,4,5,6,10,12,15,20,30,60}$ .

Common factors are $} 1, 2, 3, 4, 6, 12}$ $}1,2,3,4,6,12}$ .

Hence Greatest Common Factor is $12$ $12$ .

Answer 2 · 2016-08-24T19:40:32

$H C F = 2 \times 2 \times 3 = 12$ $HCF = 2xx2xx3 = 12$

Explanation:

A method of finding GCF and LCM - especially of several numbers if they are larger than usual - is to write the numbers as the product of the prime factors.

In this way we can immediately see which factors are common:

$\times \times \times 36 = 2 \times 2 \times 3 \times 3$ $color(white)(xxxxxx)36 = color(red)(2xx2xx3)xx3$
$\times \times \times 60 = 2 \times 2 \times 3 \times x \times 5$ $color(white)(xxxxxx)60= color(red)(2xx2xx3)color(white)(xxx)xx5$

$G C F = \times = 2 \times 2 \times 3 \times \times x = 12$ $GCF=color(white)(xx) = color(red)(2xx2xx3) color(white)(xxxxx) = 12$

$L C M = \times = 2 \times 2 \times 3 \times 3 \times 5 \times \times x = 180$ $LCM=color(white)(xx) = 2xx2xx3xx3xx5 color(white)(xxxxx) = 180$

If you have any number written as the product of its prime factors, then you know everything there is to know about that number.

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What is the GCF of 36 and 60?

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