# Math Help - divisor and remainder

1. ## divisor and remainder

(1) what is the sum of all 3 digit numbers that leave a remainder of 2 when divided by 3 ?

(2) How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?

2. 1) The least number is $101=3\cdot 33+2$
The greatest number is $998=3\cdot 332+2$
You have to calculate $\sum_{k=33}^{332}(3k+2)$

2) The least number is $103=7\cdot 14+5$
The greatest number is $999=7\cdot 142+5$
How many numbers are from 14 to 142?