Question

How do you find the GCF of $ 15 $ , $ 18 $ and $ 30 $ ?

Answer 1

Hint: As we know that GCF stands for Greatest Common Factor. When we are asked to find the greatest common factor of any two numbers, first we need to find the factors of those numbers. Factors of a number is nothing but the number that divides the given numbers without a remainder. Now, since we are given three numbers, first we will find the factors of all the three numbers $ 15 $ , $ 18 $ and $ 30 $ , then the common highest factor will be the required answer for the question.

Complete step-by-step answer:
(i)
In the question, they have asked us to find the greatest common factor of $ 15 $ , $ 18 $ and $ 30 $ .
So, first we need to find the factors of the number $ 15 $ , $ 18 $ and $ 30 $ separately.
Since, we know that factors are the numbers which divide the given number without giving any remainder or zero as a remainder.
Therefore, factors of $ 15 $ would be $ 3 $ and $ 5 $ since,
 $ 3 \times 5 = 15 $
Also, we know that $ 1 $ is the factor of all the numbers and a number is always a factor of itself. Therefore, all the factors of $ 15 $ are: $ 1 $ , $ 3 $ , $ 5 $ and $ 15 $ itself.
(ii)
Similarly, factors of $ 18 $ would be: $ 2 $ , $ 9 $ , $ 3 $ and $ 6 $ since,
 $
  2 \times 9 = 18 \\
  3 \times 6 = 18 \;
  $
Again, including $ 1 $ and the number itself, the factors obtained for $ 18 $ are : $ 1 $ , $ 2 $ , $ 3 $ , $ 6 $ , $ 9 $ and $ 18 $ itself.
(iii)
And, factors of $ 30 $ would be: $ 2 $ , $ 3 $ , $ 5 $ , $ 6 $ , $ 10 $ and $ 15 $ since,
 $
  2 \times 15 = 30 \\
  3 \times 10 = 30 \\
  5 \times 6 = 30 \;
  $
Including $ 1 $ and the number itself, the factors obtained for $ 30 $ are: $ 1 $ , $ 2 $ , $ 3 $ , $ 5 $ , $ 6 $ , $ 10 $ , $ 15 $ and $ 30 $ itself.
(iv)
Now, since we have obtained the factors of all the given numbers which are as follows:
 $ 15 $ : $ 1 $ , $ 3 $ , $ 5 $ , $ 15 $
 $ 18 $ : $ 1 $ , $ 2 $ , $ 3 $ , $ 6 $ , $ 9 $ , $ 18 $
 $ 30 $ : $ 1 $ , $ 2 $ , $ 3 $ , $ 5 $ , $ 6 $ , $ 10 $ , $ 15 $ , $ 30 $
We will look for the common factors i.e., numbers which are factors of all the three numbers given to us $ 15 $ , $ 18 $ and $ 30 $ .
Therefore, the common factors are:
 $ 1 $ and $ 3 $
Since, we are asked the greatest common factor, we can say that the greatest common factor of $ 15 $ , $ 18 $ and $ 30 $ is $ 3 $ as $ 3 $ is the greatest number in the list of common factors of all the three numbers.
So, the correct answer is “ $ 3 $ ”.

Note: If they ask for the greatest common factor, then you have to find the factors of a given number. If factors are the same in both the given numbers then you can look for the highest common factor. So, try to find factors properly, if not it may lead to wrong answers. Also, always remember that when any two numbers do not have any common factor between them, we say that the greatest common factor is $ 1 $ for those two numbers as $ 1 $ is the factor of all the numbers.