Using the fundamental theorem of arithmetic, find the HCF of 26, 51 and 91.

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

Answer: HCF of 26, 51, and 91 is 1

We will be using the fundamental theorem of arithmetic to find the HCF of 26, 51, and 91

Explanation:

According to the fundamental theorem of arithmetic, every composite number can be written as the product of the power of primes and this factorization is unique.

Represent 26, 51, and 91 as a product of its prime factors.

Prime factorization of 26 is 2 × 13

Prime factorization of 51 is 3 × 17

Prime factorization of 91 is 7 × 13

There is no common factor in the prime factorization of 26, 51, and 91

So, HCF of 26, 51, and 91 is 1.

Therefore, HCF of 26, 51, and 91 is 1.