Question

1. If r is the remainder when each of 6454, 7306, 8797 is divided by the greatest number d (d > 1) then (d - r) equal to ?​

Answer 1

Step-by-step explanation:

accordingly

a= bq+r

so when we subtract r from d then the no come which devides a completly

Answer 2

d-r=149

Step-by-step explanation:

d is the greatest number that divides the each given number and leaves same remainder  r.

Euclid algorithm

$a=bq+r$

Where $0\leq r<b$

Where a=Dividend

b=Divisor

q=Quotient

r=Remainder

By using Euclid algorithm

$6454=da+r$....(1)

$7306=db+r$...(2)

$8797=dc+r$...(3)

Subtract equation (1) from (2), equation (2) from (3) and equation (1) from (3)

$852=(b-a)d$...(4)

$1491=(c-b)d$...(5)

$2343=(c-a)d$..(6)

$852=2\times 2\times 3\times 71$

$1491=3\times 7\times 71$

$2343=3\times 11\times 71$

HCF(852,1491,2343)=213

d=213

$6454=30\times 213+64$

Remainder=r=64

$d-r=213-64=149$

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