Question

Use Euclid’s Division Algorithm to find HCF of 455 and 55.

Answer 1

Answer:

7

Step-by-step explanation:

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=42×10+35

Now, again using the Euclid division algorithm on 42 and 35, we get:

42=35×1+7

Again, applying Euclid division algorithm on 35 and 7, we get:

35=7×5+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.