What are the common factor of 63 and 135?

1 Answer
Solace M.
Sep 20, 2017

HCF#=9#
All common factors #= {1,3,9}#

Explanation:

In this question I will show all the factors and the Highest Common Factor of 63 and 125, since you don't specify which one you want.

To find all factors of 63 and 135, we simplify them into their multiples. Take 63, for instance. It can be divided by 1 to equal 63, which are our first two factors, #{1,63}#.
Next we see that 63 can be divided by 3 to equal 21, which are our next two factors, leaving us with #{1,3,21,63}#.
Finally, we see that 63 can be divided by 7 to equal 9, our last two factors, which gets us #{1,3,7,9,21,63}#. These are all the factors of 63, since there are no more pairs of integers that, when multiplied, equal 63.

We then do the same with 135 to find its factor list is #{1,3,5,9,15,27,45,135}#. Finally, we see which elements are present in both sets, which happen to be #{1,3,9}#.

The Highest Common Factor, or HCF, is the highest integer in two or more numbers which divides into these numbers to produce another integer. There are two ways to obtain the HCF. The first way is manually, by finding all the factors of 63#{1,3,7,9,21,63}#, all the factors of 135 #{1,3,5,9,15,27,45,135}#, and comparing them to see that their HCF is #9#.

The second way is by dividing both numbers#=135/63#, simplifying the fraction #=15/7#, then dividing the starting number with the new simplifiied number,
#135/15=9# or #63/7=9#,
Remembering always to divide numerator with numerator and denominator with denominator.

This process works with any two numbers which you want to find the HCF of, and can be simplified into this rule:
If#a=# any number, #b=# any number, and #c/d# is the simplified fraction of #a/b#,
The HCF#=a/c# or #=b/d#.

I hope I helped!

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