Maths question? Plz solve it..?

Question

Han sin a Chinese General devised a method to count the number of solders he had.first,he ordered his solders to form a group of 3 followed by groups of 5 and then groups of 7.In each case,he noted down the remainder,using the three remainders,he was able to calculate the exact number of solders he had without doing the actual counting. Do you know how he did it?

Answer 1

It doesn't work if the soldiers are a multiple of 105, this makes all remainders are zero, then he wouldn't know if he had 105, 210, 315 etc The same applies if the remainders are all 1 or 2. Although i suppose he must have a good guess to within a 100 of how many there are.