Question

Find the HCF of the following numbers, using the prime factorization method,
 $ 504 $ and $ 980 $

Answer 1

Hint: HCF means highest common factor. It means the greatest number which can divide the given numbers. It is also known as the greatest common divisor, and prime factorization means finding which prime numbers multiply together to make the original number.

Complete step-by-step answer:
Given: the numbers are $ 504 $ and $ 980 $
The given numbers are $ 504 $ and $ 980 $
Prime factorize the given numbers and write it as product of individual primes:
$\Rightarrow 504 = 2 \times 2 \times 2 \times 3 \times 3 \times 7 $ and
$\Rightarrow 980 = 2 \times 2 \times 5 \times 7 \times 7 $
Pairing the common one’s we have
$\Rightarrow 504 = {2^3} \times {3^2} \times 7 $ and
$\Rightarrow 980 = {2^2} \times 5 \times {7^2} $
Now, finding the common path between two numbers we get,
Common factor $ = {2^2} \times 7 $
Thus,
The HCF of the numbers $ 504 $ and $ 980 $ $ = {2^2} \times 7 $
Which is $ = 28 $

Note: In this type of questions students often make mistakes while multiplying. Do not repeat those silly mistakes. Rather than prime factorization one can find the HCF of two numbers by two more methods that is division method and factorisation method. Example of the two are
Factorization method
Let's take two numbers as $ 36 $ and $ 45 $
Thus,
Factor of $ 36 \to 1,2,3,4,6,9,12,18,36 $
 $ = 1 \times 36,\,2 \times 18,\,3 \times 12,\,4 \times 9,\,6 \times 6 $
Factor of $ 45 \to 1,3,5,9,15,45 $
 $ = 1 \times 45,\,3 \times 15,\,5 \times 9 $
Thus the highest common factor is equal to $ 9 $ .