Question

900and 270 Euclid division algorithm to find HCF

Answer 1

Euclid's division algorithm:

a = bq + r such that 0≤r<b ————>(1)

here a and b are nothing but a is divided by b, then q and r are quotient and remainder respectively.

let us take bigger number as 'a'

a = 900

smaller number as 'b'

b = 270

equation (1) becomes,

900 = 270q + r let us now divide 900 by 270 where q = 3 r = 90

900 = 270×3 + 90

The remainder is 90 ≠ 0

Applying Euclid's division algorithm to the divisor 270 and remainder 90, we get

270 = 90×3+0

The remainder at this stage = 0

The divisor at this stage = 90

Therefore Highest Common Factor of 900, 270 =

90

Hope this is helpful❤

Note:

The above algorithm will always produce remainder zero at some stage. Hence the algorithm should terminate. The divisor at the last stage is your HCF