Question

What is the H.C.F. of 242, 484 and 363?

Answer 1

Hint: Here, we are required to find the H.C.F. of the given three numbers. We will find the factors of the three numbers by using the prime factorization method and multiplying the factors which are common in all the three numbers will give us the highest common factor (H.C.F.) of the three numbers.

Complete step-by-step answer:
We have to find the H.C.F. of three numbers. A Highest common factor (H.C.F.) is the greatest number that is a factor of two or more numbers. This is also known as the Greatest Common Factor (G.C.F.).
By using the prime factorization method, we will find the factor of the given three numbers.

Therefore, We can write 242 as:
\[242 = 2 \times 11 \times 11\]

Therefore, we can write 484 as:
\[484 = 2 \times 2 \times 11 \times 11\]

Therefore, we can write 363 as:
\[363 = 3 \times 11 \times 11\]
Now, as we can see, the common factor in all the three numbers is
\[11 \times 11 = 121\]
This is because, in all the three numbers, we can find the number 11 multiplying 2 times with all the other factors. Hence, 121 is the highest common factor of the given three numbers.
Therefore, H.C.F. of 242, 484 and 363 is 121.

Note: The other way to solve this question is by using division method.
First of all, we will find the H.C.F. of the first two numbers by division method.
Hence, dividing 484 by 242, we get:

Since the remainder is 0, therefore, the H.C.F. of 484 and 242 is 242.
Now, we will divide the third number by the H.C.F. of first and second number.
Hence, dividing 363 by 242, we get,

Since, the remainder is 121, therefore, the H.C.F. of 484 and 242 is 121.
Hence, this is the required answer.