What is the GCF of 225 and 315?

2 Answers
Apr 7, 2016

45

Explanation:

List the factors of 225 and 315 and find the highest one that both share.

You could also do it by realising that the GCF of 225 and 315 also has to be a factor of the difference between the two of them. In other words, the factor has to go into 90, because otherwise you would have no way of linking 225 to 315 with whole numbers. And the greatest factor of one (even) number is half of it, which means 90/2 = 45 is a great suspect for the GCF. It's as good a starting point as any, and in this case turns out to be right.

Sep 2, 2016

GCF = 3xx3xx4=5 = 45

Explanation:

In most cases we should be able to find the GCF fairly easily by just knowing the multiplication tables up to 12 x 12. Sometimes a bigger number might be included which we do not know well. This is just such a case.

It is obvious that 5 is a common factor, but without some working we cannot decide on a bigger factor.
You might recognise 225 " as " 15^2

In order to find the GCF (and the LCM) write each number as the product of its prime factors.

color(white)(xxxx) 225 = 3xx3xx5xx5
color(white)(xxxx) 315 = 3xx3xx5color(white)(xxx)xx7

GCF =color(white)(xxx)3xx3xx5 color(white)(xxxxxx)=45

From this it is very clear that the common factors are 3x3 x5.

If we needed the LCM as well it can be calculated easily from this format:
Include each column of factors, do not count factors that are in the same column twice.

LCM = 3xx3xx5xx5xx7 = 1575