Question

Find the HCF of 96 and 404 by the Prime Factorization Method.

Answer 1

Hint: Use prime factorization method to obtain the prime factors of 96 and 104. Then, find the common factors and multiply them to get the HCF.

Complete step-by-step answer:

The HCF or the Highest Common Factor is the greatest number that can divide the given number. It is also known as the Greatest Common Divisor (GCD).

We can find the HCF of a number using the prime factorization method.

In this method, we start dividing the number by the first prime number and continue dividing by 2 until we get a remainder. Then we proceed with next prime number 3 and so on. Then represent the number as the product of prime number as obtained. Then find the common factors between both the number and multiply them to obtain the HCF.

Now, let us prime factorize the number 96.

Let us prime factorise 404.

So, we can write 96 and 404 as the product of their respective prime numbers.

\[96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3\]

\[404 = 2 \times 2 \times 101\]

The common prime factors between the two numbers are 2, 2.

Then the HCF is the product of the common prime factor and is given as follows:

HCF = \[2 \times 2\]

HCF = 4

Hence, the HCF of 96 and 404 is 4.


Note: You may spend some time to check out if 101 is a prime number or not, because if it can be factored further, then it needs to be factorized.