Use Euclid’s division algorithm to find the HCF of the following numbers: 55 and 210.

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answer is A.

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Detailed Solution

Concept- Given two positive numbers a and b, Euclid's division lemma states that there are only two distinct integers q and r such that a = bq+r. The quotient is the number q, while the remainder is the number. Dividend and divisor are terms that refer to the numbers a and b, respectively.
Considering the figures 55 and 210
The size is 55 x 210.
multiplying 210 by 55.
Given two positive numbers a and b, Euclid's division lemma states that there are only two distinct integers q and r such that a = bq + r.
The quotient is the number q, while the remainder is the number r.
Dividend and divisor are terms that refer to the numbers a and b, respectively.
210 divided by 55 yields 3 as the quotient and 45 as the remainder.
Therefore, we can write 210 = 553 + 45.
Divide 55 once more using the leftover 45.
We obtain a quotient of 1 and a remainder of 10.
Therefore, we can write 55 = 451+10
We once more use the division lemma because we have a non-zero remainder.
45 divided by the new remaining 10 gives us,
45 = 10×4+5
Once more, the remainder is not zero.
When we divide 10 by 5, we get 10=52+0.
As a result, the remaining is zero. There can be no more division, therefore.
The final non-zero remainder, which equals 5, is the HCF.
Hence, the correct answer is option 1.

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