Question

find the sum of all integers between 1000 and 2000 which are disible by 10​

Answer 1

Answer:

If a number is divisible by 9, it is also divisible by 3, so we don’t need to consider 3. We’re left with 4, 7 and 9. Now these numbers are relatively prime (have no common divisors), so any number divisible by all three must be divisible by their product 4*7*9 = 252.

So we’re looking for multiples of 252 between 1,000 and 2,000.

Now 4*252 = 1,008 is in the range, while 8*252 = 2,016 is just outside.

So the 4th, 5th, 6th and 7th multiple of 252 are between 1,000 and 2,000.

The answer is four.