Question

Find the HCF of 55, 60, 66, 72, 96.

Answer 1

Hint: We need to find the HCF of 55, 60, 66, 72, 96. First we need to find the common factors of 55, 60, 66, 72, 96 from their factors’ list. Then we find the greatest common factor of 55, 60, 66, 72, 96. We can also take the simultaneous factorisation of those two numbers to find the HCF.

Complete step by step solution:
We need to find the HCF of 55, 60, 66, 72, 96. HCF stands for highest common factor.
we first find the factors of 55, 60, 66, 72, 96.
The factors of 55 are $ 1,5,11,55 $ .
The factors of 60 are $ 1,2,3,4,5,6,10,12,15,20,30,60 $ .
The factors of 66 are $ 1,2,3,6,11,22,33,66 $ .
The factors of 72 are $ 1,2,3,4,6,8,9,12,18,24,36,72 $ .
The factors of 96 are $ 1,2,3,4,6,8,12,16,24,32,48,96 $ .
The common factors of 55, 60, 66, 72, 96 is 1. It is also the highest one.
The greatest common factor of 55, 60, 66, 72, 96 is 1.
We also can use the simultaneous factorisation to find the greatest common factor of 14 and 21.
We have to divide both of them with possible primes which can divide both of them.
\[1\left| \!{\underline {\,
  55,60,66,72,96 \,}} \right. \]
The only possible prime being 1. Therefore, the greatest common factor of 55, 60, 66, 72, 96 is 1.
So, the correct answer is “1”.

Note: We need to remember that the HCF has to be only one number. It is the greatest possible divisor of all the given numbers. If the given numbers are prime numbers then the HCD of those numbers will always be 1.
Therefore, if for numbers $ x $ and $ y $ , the GCD is $ a $ then the GCD of the numbers $ \dfrac{x}{a} $ and $ \dfrac{y}{a} $ will be 1.