Given,

Now (25 190 - 19 190 ), 8 190 , 2 190 are divisible by 2, as 25 190 will give remainder as 1 and 19 190 will give remainder as 1 when divided by 2, so combined 25 190 - 19 190 will give remainder 0

Now, (25 190 - 8 190 ) & (-19 190 + 2 190 ) are divisible by 17, a n - b n is divisible by a - b if n is even,

So given number is divisible by 34 as it is divisible by 2 & 17 both,

Now,25 190 = (7x3 + 4) 190 , dividing by 7 we get,

(7x3 + 4) 190 = 4 190 = 16 95 = 2 95 = 4 . 8 31

Now when 4 . (7 + 1) 31 divided by 7 will give remainder as 4 . 1 = 4

And 19 190 = (7x3- 2) 190 , when divided by 7 we get,

(7 x 3 - 2) 190 = (-2) 190 = 2 190 = 2 x 8 63 = 2 x (7 + 1) 63

So, when 2 x (7 + 1) divided by 7 will give remainder as 2

Similarly 8 190 = (7 + 1) 190 will give 1 remainder

And 2 190 = 2(7+I) 63 will give 1 remainder,

So combining all we get,25 190 - 19 190 - 8 190 + 2 190 = 4-2-1 + 1 = 5

Not divisible by 7, so it will not be divisible by 14

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