Find the least natural number larger than 100 which leave the remainder 12 when divided by 19.

Question

Philoid · Accepted Answer

Since we have to find a number greater than 100

So first we will find the quotient and remainder for 100 when divided by 19

Here s = 100

We know If s → (q, r) denotes the quotient q and r denotes the remainder r

Then s = (b × q) + r where s and b > 0 and 0 ≤ r < b

When s is divided by 19 then

100 = 19 × 5 + 5

Here the quotient = 5 and r = 5

But the remainder has to be 12 so the 5+ 7 = 12

So the least natural number 107 (100 +7)