The HCF of 455 and 42 using Euclid algorithm is

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answer is A.

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Detailed Solution

Concept- Euclid’s Division algorithm is a method for determining the highest common factor between any given pair or trio of positive numbers.
Euclid’s Division lemma states that for any two positive integers say a and b there exist two distinct whole numbers say q and r, such that,

.
In this question, the given numbers are 455 and 42.
By applying Euclid’s division lemma for 455 and 42, we get
Here, we have

So, now we will take the new dividend as 42 and divisor as 35.
Again, by applying Euclid’s division lemma for 42 and 35, we get
Here, we have

So again, we will take the new dividend as 35 and divisor as 7.
By applying Euclid’s division lemma for 35 and 7, we get
Here, we have

Here, we will obtain 0 as remainder and 7 as divisor.
As a result, the HCF of 455 and 42 is 7.
Hence, the correct answer is option (1).

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