Question

Find the remainder of 235*157*90/7
using Euclid's division lemma without using multiplication.

Answer 1

the number is 235*157*90

235 = (33*7+4)

157 = 22*7+3

90 = 12*7+6

therefore 235*157*90 = (33*7+4)*(22*7+3)*(12*7+6)

thus other than 4*3*6 each term is divisible by 7.

thus the required remainder is same , when we divide 4*3*6 by 7.

4*3*6 = 12*6 = (7+5)*6=7*6+5*6

the remainder is equal to the remainder, when we divide 5*6 by 7 i.e. 30 by 7.

30 = 7*4 +2

thus the required remainder = 2.

hope this helps you.

Answer 2

Answer:

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