Find the H.C.F by prime factorization method
1. 60, 96, 150
2. 63, 35, 56

Given :

The given numbers are (1). 60, 96, 150. (2). 63, 35, 56.
 

To do :

We have to find the HCF of the given numbers by prime factorization.

Solution :

1.Prime factorization of 60, 96, 150.

Prime factors of $60 = 2 \times 2 \times 3 \times 5 = 2^2 \times 3 \times 5$

Prime factors of $96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times3 $

Prime factors of $150 = 2 \times 3 \times 5 \times 5 = 2 \times 3 \times 5^2$

$$HCF = Lowest powers of common prime factors$$

HCF $= 2 \times 3 = 6$

Therefore, HCF of 60, 96, 150 is 6.  

2. Prime factorization of 63, 35, 56.

Prime factors of $63 = 3 \times 3 \times 7 = 3^2 \times 7$

Prime factors of $35 = 5 \times 7$

Prime factors of $56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7$

$$HCF = Lowest powers of common prime factors$$

HCF $= 7$

Therefore, HCF of 63, 35, 56 is 7.  

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Updated on: 10-Oct-2022

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