What is the GCF of 36 and 60?

2 Answers
Mar 31, 2016

Answer:

Explanation:

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

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

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

Hence Greatest Common Factor is #12#.

Aug 24, 2016

Answer:

#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:

#color(white)(xxxxxx)36 = color(red)(2xx2xx3)xx3#
#color(white)(xxxxxx)60= color(red)(2xx2xx3)color(white)(xxx)xx5#

#GCF=color(white)(xx) = color(red)(2xx2xx3) color(white)(xxxxx) = 12#

#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.