Question

what least number should be subtracted from 1000 so that 43 exactly divides the difference ?

Answer 1

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= 35×28+20

Subtracting 20 from both sides,

1000–20=35×28+20–20

Thus, 980=35×28

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

And so, 20 is the smallest number to be subtracted.

Answer 2

hEya hEre iS uR aNs....
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The least number subtracted should be
a=bq+r
1000=43×23+11
subtracting 11 from both sides
1000-11=43×23+11-11
989=43×23
so least no. is 11
hope it helps u...