Question

1. Find the H.C.F. of the following numbers using prime factorization method.
(i) 106, 159, 265

GIVE ME ANS STEP BY STEP​

Answer 1

Answer: HCF of 106, 159, and 265 is 53.

Answer 2

Answer:

The largest possible number which divides the given numbers exactly without leaving any remainder is called the HCF (Highest Common Factor).

Answer: HCF of 106, 159, and 265 is 53

HCF of 106, 159, and 265 is the highest number that divides 106, 159, and 265 exactly leaving the remainder 0.

Explanation:

We will show two methods to find the HCF (106, 159, 265).

HCF of 106, 159, and 265 by Listing the Common Factors

HCF of 106, 159, and 265 by Prime Factorization

Method 1: Calculate HCF of 106, 159, and 265 by Listing the Common Factors

The factors of 106, 159, and 265 are shown below.

HCF of 106, 159, and 265

Clearly, the common factors of 106, 159, and 265 are 1 and 53

The highest common factor of 106, 159, and 265 is 53

Method 2: Calculate HCF of 106, 159, and 265 by Prime Factorization

Let us represent 106, 159, and 265 as a product of its prime factors.

Prime factorization of 106 is 2 × 53

Prime factorization of 159 is 3 × 53

Prime factorization of 265 is 5 × 53

The common factor in the prime factorization of 106, 159, and 265 is 53.

So, HCF of 106, 159, and 265 is 53.

The solution of HCF of 90 and 105 will be the same from both the above methods.

Therefore, HCF of 106, 159, and 265 is 53.