Question

Find the greatest number that will divide 65, 81 and 145 leaving the same remainder in each case.

please answer fast and explain as well.

Answer 1

Answer:

145 - 65 =80

145 - 81 = 64

81 - 65 =16

Now find the HCF of 80,64,16

80 = 16*5 = 2*2*2*2*5

64=2*2*2*2*2*2

16=2*2*2*2

So HCF is 16.

hence 16 is the only largest no. which divides the 65,81,145 leaving 1 as the remainder in every case

hope it helps