Which least number should be subtracted from 10000 so that the difference is exactly divisible by 35?

Given :

The given statement is least number should be subtracted from 1000, so that the difference is exactly divisible by 35.

To find :

We have to find the least number.

Solution :

According to Euclid's division algorithm,

$a=bq+r$

Where,

a= dividend

b=divisor

q=quotient and

r=remainder.

So let a=1000, b=35,

So we get,

$1000= 35\times 28+20$

Subtracting 20 from both sides,

$1000–20=35\times28+20–20$

Thus, $980=35\times 28$

Therefore, as seen above, 980 is perfectly divisible by 35.

And so, 20 is the smallest number to be subtracted from 1000 so that the difference is exactly divisible by 35.

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