Question

How many numbers, lying between 300
500, are divisible by 17?
(b) 38
(c) 41
(a) 40
(d) 4​

Answer 1

First let us divide the number 300 by 17.

We get,

300/17 = 17 x 17 + 11

Since the remainder is 11, the next multiple of 17 would be

(300 +6) = 306306 = 17 x 18

Now dividing 900 by 17 we get,

500/17 = 17×29+7

Since the remainder is 7 only 10 needs to be added to 500 to get the next multiple.

So 510 is a multiple of 17.

But we need numbers between 300 and 500.

So the previous multiple is

510 - 17 = 493493 = 17 X 29

Since the first 18th multiple is above 300, that means we can ignore the previous 17 multiples of 17.

So, 29 - 17 = 12

There are 12 numbers lying between 300 and 500 that are divisible by 17.