Question

What is the greatest common divisor of $ 20 $ and $ 36 $ ?

Answer 1

Hint: The greatest common divisor of two given numbers is the greatest number which divided completely both the numbers. For example $ 2 $ is greatest common divisor of $ 4{\text{ and 6}} $ since there is no other factors of $ 4{\text{ and 6}} $ which are greater than $ 2 $ and are common to both of them. The greatest common divisor
Of two numbers are found out by first factoring the numbers into its prime factors instead of its normal factors, and then finding out the factors which are common to both of them and then multiplying those factors with each other. This process will get us what we call as the greatest common divisor.

Complete step by step solution:
The greatest common divisor of two given numbers is the greatest number which divided completely both the numbers
First we will prime factorize $ 20 $ we write the prime factorization of a given number as
 $ 20 = 2\times2\times5 $
Similarly for the prime factorization of $ 36 $ we write,
 $ 36 = 2\times2\times3\times3 $
Since $ 2\times2 $ is common for both the numbers we can write,
 $ 4 $ as the greatest common divisor.
So, the correct answer is “4”.

Note: The greatest common divisor of two numbers is also called to be the highest common factor of two numbers. Thus $ HCF = GCD $ of two numbers. There is also a very interesting relation between the highest common factor or the greatest common divisor with the least common multiple the relation is as follows,
 $ product{\text{ }}of{\text{ }}number = (LCM) \times (HCF) $
Which means product of any given number is equal to the multiplication of the highest common factor and the least common multiple of two numbers in question