Maths Olympiad - Prime Factors 1

Question:

When 2007 bars of soap are packed into N boxes, there is a remainder of 5. How many possible values of N are there?

Answer:

No. of bars of soap to be divided equally among the boxes = 2007 - 5 = 2002



2002 = 2 x 11 x 7 x 13

Therefore, N, the no. of boxes could be a combination of these prime factors
= 2, 7, 11, 13, 14 (2x7), 22 (2x11), 26 (2x13), 77 (7x11), 91 (7x13), 143 (13x11), 154 (2x7x11), 182 (2x7x13), 286 (2x11x13), 1001 (7x11x13)

*Note: You do not actually need to multiply these factors because it's not required for this question.

Counting the no. of boxes that could divide 2002 bars of soaps equally = 14
Therefore, N = 14