Question

How do you find the Greatest Common Factor of \[14,42,91\]?

Answer 1

Hint: We use the concepts of greatest common factor or greatest common divisor to solve this problem. We will know about factors and GCD in detail while solving this problem. We will look at some examples and find the HCF of those examples, and using those examples, we will solve this problem.

Complete step by step answer:
In mathematics, the Greatest Common Factor (GCF or GCD) of two or more numbers is defined as the greatest number among the common divisors or factors of those numbers. It is also called the Greater Common Divisor.
A factor or a divisor is a value which divides a number exactly i.e., which divides a number with remainder 0.
For, example, take the numbers 36 and 60.
The factors of 36 are \[1,2,3,4,6,9,12,18,36\]
The factors of 60 are \[1,2,3,4,5,6,10,12,15,20,30,60\]
So, the common factors of 36 and 60 are \[1,2,3,4,6,12\]
So, the greatest among these common divisors is called Greatest Common Factor.
So, here, the Greatest Common Factor of 36 and 60 is 12.
Now, in the question, we have to find the GCD of 14, 42 and 91.
The factors of 14 are \[1,2,7,14\]
The factors of 42 are \[1,2,3,6,7,14,21,42\]
The factors of 91 are \[1,7,13,91\]
So, the common factors of 14, 42 and 91 are \[1,7\]
And the greatest among the common factors is 7.
So, the Greatest Common Factor of 14, 42 and 91 is 7.

Note:
Greatest Common Divisor is also called the Highest Common Factor (HCF).
We have to consider ONLY the greatest value among the common factors in order to get GCD.
The number 1 will be a common divisor or factor for all numbers, and the numbers with GCD as 1 are called co-primes.