Use Euclid’s Division Algorithm to find the HCF of 10244 and 9648.
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Step-by-step explanation:
We need to find the HCF of 10224 and 9648, using Euclid's division algorithm.
Upon dividing a by b, Euclid's Lemma states that
A = bq + r, where
where q is the quotient and r the remainder.
In addition, Euclid's Lemma states that the HCF of a and b is equal to the HCF of b and r.
In this problem, a = 10224 and b = 9648.
Applying the division algorithm, we get
10224 = 9648 × 2 + 576
9648 = 576 × 16 + 432 (continuing the division algorithm with 9648 and 576)
574 = 432 × 1 + 144
432 = 144 × 3 + 0
Therefore, the HCF of 10224 and 9648 is 144.
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