Q. 1 C4.4( 43 Votes )
Use Euclid’s division algorithm to find the HCF of
1651 and 2032
Answer :
Euclid’s Division is a method for finding the HCF (highest common factor) of two given integers. According to Euclid’s Division Algorithm, For any two positive integers, ‘a’ and ‘b’, there exists a unique pair of integers ‘q’ and ‘r’ which satisfy the relation:
a = bq + r , 0 ≤ r ≤ b
Given integers 1651 and 2032. Clearly 2032>1651.
By applying division lemma
⇒ 2032 = 1651×1 + 381
Since remainder 
0, applying division lemma on 1651 and 381
⇒ 1651 = 381×4 + 127
Since remainder 
0, applying division lemma on 381 and 127
⇒ 381 = 127×3 + 0
Since remainder = 0,
∴ the HCF of 1651 and 2032 is 127.
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