Question

what is Euclid formula​

Answer 1

Step-by-step explanation:

a=bq+r ,

where a=dividend

b=divisor

q=quotient

r=remainder

and 0<and equal to r

and r is smaller than b....

Answer 2

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

$a = bq + r \: where \: 0 \leqslant r < b$

●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,

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

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.