Question

Find the H.C.F of the following: 256, 442, and 940.

Answer 1

Hint: In this question, to find H.C.F of 256, 442 and 940, we have to write each number as a product of prime factors. Multiply all the common prime factors having lowest degree.

Complete step-by-step answer:
Step 1: find the prime factors of 256, 442, 940
$256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {2^8}$
$442 = 2 \times 13 \times 17$
$940 = 2 \times 2 \times 5 \times 47 = {2^2} \times 5 \times 47$
Step 2: multiply all the common prime factors with the lowest degree. Here we have only 2 as a common prime factor with the lowest power of 1.
Therefore, the H.C.F of 256, 442, and 940 = 2.

Note: There are two methods to find the HCF (highest common factor) of the numbers are Prime factorization method and Division Method. We have already seen the prime factorization method above. We can findH.C.F. by Long Division Method
To find the H.C.F. of the given number we will follow the following steps:
We divide the bigger number by the smaller number.
Divide the smaller number in step 1 with remainder obtained in step 1.
Divide divisor of second step with remainder obtained in step 2.
We will continue this process until we get the remainder zero and the divisor obtained in end is the required H.C.F.
Finding the highest common factor (H.C.F) by prime factorization for a large number is not very convenient. The method of long division is more useful for large numbers.