Question

The HCF of 455 and 42 using Euclid algorithm is
(a) 7
(b) 6
(c) 5
(d) 4

Answer 1

Hint: Here, we will apply the Euclid division algorithm on 455 and 42 to find their HCF. First of all, we will write 455 in the form of $42q+r$, where q and r are integers and r is always less than 42. We will continue this process over and over again till a zero remainder is obtained. The last non-zero remainder obtained in this process will be the HCF of the given number.

Complete step-by-step answer:
Euclid’s division algorithm requires the application of Euclid’s division lemma continuously. Euclid’s division lemma states that:
Any positive real number ‘a’ can be represented as $a=bq+r$, where ‘b’ is greater than 0 and is called the divisor of ‘a’ and ‘r’ is remainder obtained after dividing ‘a’ by ‘b’.
Since, the numbers given here are 455 and 42.
So, first of all we will write 455 as:
$455=42\times 10+35$
Now, again using the Euclid division algorithm on 42 and 35, we get:
$42=35\times 1+7$
Again, applying Euclid division algorithm on 35 and 7, we get:
$35=7\times 5+0$
So, we get a 0 remainder here which means that we will stop this process here, that is, we will stop applying the Euclid division algorithm further.
Since, the last non-zero remainder that is obtained in the process is 7, this means that the HCF of 455 and 42 is 7.
Hence, option (a) is the correct answer.

Note: Here, a confusion that may arise is what would be the HCF of two numbers if a zero remainder is obtained in the first step. In such cases, the smaller of the two numbers is their HCF.