Question

find the great greatest number which divides 285 and 1245 leaving the same remainder 5 in each case

Answer 1

Given : number which divides 285 and 1245 leaving the same remainder 5 in each case

To find : great greatest number

Solution:

Let say the greatest Number is N which divides 285 and 1245 leaving the same remainder 5 in each case

=> 285 = AN + 5

& 1485 = BN + 5

=> AN = 280    & BN = 1480

=> N is the HCF of 280  & 1480

1480 = 280 * 5  + 80

280  = 80*3  + 40

80 = 40 * 2

40 is the HCF

Hence N = 40

40 is the greatest Number which divides 285 and 1245 leaving the same remainder 5 in each case

285 = 40*7 + 5

1485 = 40*37 + 5

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