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Using Euclid's division algorithm, find the HCF of the numbers 466 and 361 .

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answer is C.

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Detailed Solution

Given,
The numbers are 466 and 361.
Let

a = 466

and

b = 361

,
Now as we know,
Euclid division lemma states that if we have two numbers a and b, then there exist unique integers p and q which satisfies the condition

a = b q + r, 0 ≤ r < b

.
Using Euclid division lemma algorithm, we get,

⇒ 466 = 361 × 1 + 105

⇒ 361 = 105 × 3 + 46

⇒ 105 = 46 × 2 + 13

⇒ 46 = 13 × 3 + 7

⇒ 13 = 7 × 1 + 6

⇒ 7 = 6 × 1 + 1

⇒ 6 = 1 × 6 + 0

⇒ H C F = 1

Therefore H.C.F of 466 and 361 is 1.
Therefore, option(3) is correct answer.

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