Divides means no remainder

Does 4 divide 36? Yes: share 36 sweets among groups of 4 and nothing is left over, so the remainder is 0. That is all "divides" means.

The lazy way is to test every number from 1 up to n. For n near a trillion that is a trillion checks, hours of running, so we need something smarter.

Remainder 0: means the number divides evenly.

In code

36 % 4   # 0, so 4 divides 36
36 % 5   # 1, so 5 does not

n = 36 · try i while i × i ≤ 36

36 % 1 = 0. A hit, and it brings its partner 36 ÷ 1 = 36. Two divisors.

Move 1 of 6

Every small divisor has a big partner

Divisors come in pairs. Since 4 divides 36, so does 36 ÷ 4 = 9. For 36 the pairs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 with itself.

Each pair has one member no bigger than the square root, so you only test numbers while their square stays within n, and every hit counts for two.

Stop: once the number times itself passes n. No square roots needed.

When the number times itself equals n: the pair is one number. Count it once.

In code

count = 0
i = 1
while i * i <= n:
    if n % i == 0:
        count += 1 if i * i == n else 2
    i += 1
return count