Question

HCF of 95 and 152 is:
A. 1
B. 19
C. 57
D. 38

Answer 1

Hint: Here, we will find the factors of the two numbers by using the prime factorization method. Then we will multiply the factors which are common in both the numbers to get the required highest common factor (H.C.F.) of the two numbers.

Complete step-by-step answer:
We have to find the H.C.F. of two numbers. A Highest common factor (H.C.F.) is the greatest number that is a factor of two or more numbers. This is also known as the Greatest Common Factor (G.C.F.).
By using the prime factorization method, we will find the factor of the given two numbers.
Now we will factorize 95.
So, dividing 95 by the prime number \[5\], we get
\[95 \div 5 = 19\]
Hence, 95 can be written as:
\[95 = 5 \times 19\]
Now we will factorize 152.
We can see that 152 is an even number, so dividing it by the least prime number 2, we get
\[152 \div 2 = 76\]
Now dividing 76 by 2, we get
\[76 \div 2 = 38\]
Dividing 38 by 2, we get
\[38 \div 2 = 19\]
Hence, 152 can be written as:
\[152 = 2 \times 2 \times 2 \times 19\]
In both the numbers, we can find the number 19 multiplying with all the other factors. Hence, 19 is the highest common factor of the given two numbers.
Therefore, H.C.F. of 95 and 152 is 19.

Hence, option B is the correct answer.

Note:
In order to find HCF of two numbers it is important to express those numbers as a product of their prime factors. Prime factors are those factors which are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself. Now, in order to express the given number as a product of its prime factors, we are required to do the prime factorization of the given number. Factorization is a method of writing an original number as the product of its various factors.