Between 75 and 200
Multiple of 15
Factor of 2700
When divided by 10 remainder is 5
The number is 150.
Explanation:
- It is between 75 and 200, which means that it is in the range of (75, 200).
- It is a multiple of 15, which means that it can be written as 15x for some integer x.
- It is a factor of 2700, which means that it divides evenly into 2700. We can write 2700 as 15*15*12*2, so the factors of 2700 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 36, 50, 60, 75, 100, 150, 180, 225, 300, 450, 900. The only factor of 2700 that is between 75 and 200 and a multiple of 15 is 150.
- When divided by 10, the remainder is 5. This means that the number has the form 10x + 5 for some integer x. We can check that 10x + 5 is divisible by 15 if and only if x is odd. Since 150 has the form 10*15 + 5, which is odd, it satisfies this condition.