Question

What is the greatest common factor for 27 and 36?
(a) 7
(b) 8
(c) 9
(d) None of these

Answer 1

Hint: In our given problem, we are here trying to find out the greatest common divisor of two given numbers. We will start by factoring the numbers one after one. Then, we will try to find the common factors and multiply them to get our result.

Complete step by step solution:
According to the problem, we are trying to find the greatest common factor for 27 and 36.
So, to start with, we are given two numbers 27 and 36.
For finding the GCD or the greatest common factor, we have to start by factoring the numbers one after another.
In case of 27, we are having, $27=3\times 3\times 3$
And by factoring 36, we are getting, $36=2\times 2\times 3\times 3$
We will try to get the common factors between them and also find which one of them is the greatest.
So, we can easily see the common factors of the given numbers in 2 and 3.
We will get our needed result multiplying these terms.
Our greatest common divisor of those numbers 27 and 36 is, $3\times 3=9$ .
Hence, the greatest common divisor of 27 and 36 is 9.

So, the correct answer is “Option c”.

Note: In this problem, we have used the greatest common divisor of two given numbers. In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include greatest common factor (gcf).