Question

Find the HCF of $91$ and $112$ and $49$

Answer 1

Hint : First, we shall learn about HCF. HCF is the largest common factor of all the given numbers and HCF stands for Highest Common Factor. We calculate the HCF for the given numbers using three methods.
Factorization method
Prime factorization method
Division method
Here in this problem, we shall use the factorization method to calculate the HCF.

Complete step-by-step solution:
To find the HCF using the factorization method, we need to follow the steps given below.
a) We need to list down the factors for the given numbers.
b) Then we shall choose the largest common factor among the listed factors and the chosen factor is the required HCF.
The given numbers are $91$ , $112$ and $49$
We are asked to calculate the HCF for the given numbers.
Let us consider the number $91$
We need to obtain the factors for $91$
$
  7\left| \!{\underline {\,
  {91} \,}} \right. \\
  13\left| \!{\underline {\,
  {13} \,}} \right. \\
 $
Hence, the factors $91$ are $7and13$
Now let us consider the number $112$
We need to obtain the factors for $112$
$
  2\left| \!{\underline {\,
  {112} \,}} \right. \\
  2\left| \!{\underline {\,
  {56} \,}} \right. \\
  2\left| \!{\underline {\,
  {28} \,}} \right. \\
  7\left| \!{\underline {\,
  {14} \,}} \right. \\
  2\left| \!{\underline {\,
  2 \,}} \right. \\
 $
Hence, the factors for $112$ are $2,2,2,2,7$
Now let us consider the number $49$
We need to obtain the factors for $49$
$
  7\left| \!{\underline {\,
  {49} \,}} \right. \\
  7\left| \!{\underline {\,
  7 \,}} \right. \\
 $
Hence, the factors for $49$ are $7,7$
Therefore, while analyzing the listed factors, we have got the largest common factor $7$
Hence, $7$ is the required HCF for the given numbers.
Note: HCF is the largest common factor of all the given numbers and HCF stands for Highest Common Factor. To find the HCF using the factorization method, we need to follow the steps given below.
a) We need to list down the factors for the given numbers.
b) Then we shall choose the largest common factor among the listed factors and the chosen factor is the required HCF.