General Exercises

1. How many divisor does 504 have in ℕ?

2. What's the sum of the numbers from 50 to 250 (extremes included)?

Solutions

1. The factorizarion of 504 is 7 ⋅ 3² ⋅ 2³. We can count the number of ways to pick i, j, k such that 7ⁱ ⋅ 3^j ⋅ 2^k divides 7 ⋅ 3² ⋅ 2³: We have 2 choices for i, 3 choices for j, and 4 choices for k. Thus 24 divisors.  ■

2. 250 ⋅ 151/2 = 18875.  ■