Question

Find the HCF of 12576 and 4052 by using the prime factorisation method.

Answer 1

Hint- Here, we will proceed by representing the given numbers as the product of the prime factors of those numbers and then finding out the prime factors which are common these two numbers whose HCF is required.

Complete step-by-step answer:
According to prime factorisation method, the number 12576 can be represented as the product of prime factors as shown under
$12576 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 131$
Similarly, using the prime factorisation method the number 4052 can be represented as the product of prime factors as shown under
$4052 = 2 \times 2 \times 1013$
In order to find the highest common factor (HCF) between the given numbers, we will take the product of the prime factors which are common to both these given numbers i.e., 12576 and 4052.
Clearly, there are two same prime factors common among the prime factors of the numbers 12576 and 4052.
HCF of 12576 and 4052 =$2 \times 2$=4
Therefore, the HCF of the two numbers i.e., 12576 and 4052 is 4.

Note- Prime factors of any given number are the numbers which are prime numbers (i.e., the numbers which are only divisible by 1 and that number itself) and are completely divisible by the given number. This means that when the given number is divided by any of the prime factors of that given number, the remainder will always be zero.