Question

Find the greatest no which can divide 76,132,160 ans same remainder

Answer 1

hey mate

here is your answer.

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Suppose the greatest number which can divide 76,132 and 160 is p and reminder be r Also the quotient be q1,q2 and q3 for 76,132 and 160 respectively Thus pq1+r=76. (1) pq2+r=132. (2) pq3+r=160. (3) From 1,2 and 3 we get P(q2-q1)=132-76=56 P(q3-q2)=160-132=28 P(q3-q1)=160-76=84 Therefore the hcf of 56,28 and 84 are 56=2*2*2*7 28=2*2*7 84=2*2*3*7 HCF=2*2*7=28 Therefore the greatest which can divide 76,132 and 160 and leave the same reminder is 28