Question

WHAT IS EUCLID'S FORMULA
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Answer 1

Answer:

Euclid's division algorithm is a way to find the HCF of two numbers by using Euclid's division lemma. It states that if there are any two integers a and b, there exists q and r such that it satisfies the given condition a = bq + r where 0 ≤ r < b.

Answer 2

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WHAT IS EUCLID'S FORMULA

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Euclid's Algorithm/Division algorithm/Division lemma : For each pair of positive integers a and b(dividend and divisor respectively),we can find the whole numbers q and r (quotient and remainder respectively)satisfying the relation

a = bq + r \: where \: 0 \leqslant r < ba=bq+rwhere0⩽r<b

●Euclid's algorithm is a technique to compute the Highest Common Factor (HCF) of two given integers.

Example:

Find the HCF of 60 and 100.

By Euclid's algorithm,

a = bq + r \: (0 \leqslant r < b)a=bq+r(0⩽r<b)

Where a = 100, b = 60

When 100 is divided by 60,the remainder is 40.

100 = (60×1)+40

Now the division of 60 with the remainder 40 in the above equation and apply the division algorithm.

60=(40×1)+20

Now consider the division of 40 with the remainder 20,and apply the division algorithm.

40=(20×2)+0

The remainder has became zero and we cannot proceed any further. Therefore the HCF of 60 and 100 is 20.

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