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Counting Factors

Is there an efficient way to work out how many factors a large number has?

Summing Consecutive Numbers

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Thirty Six Exactly

Age 11 to 14 Challenge Level:

The number $12 = 2^2 \times 3$ has 6 factors. What is the smallest natural number with exactly 36 factors?