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Counting Factors

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

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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?

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Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Summing Consecutive Numbers

Age 11 to 14 Challenge Level:
Start by trying some simple cases; perhaps start by exploring what happens when you add two or three consecutive numbers.

$1 + 2 + 3 = 6$

$2 + 3 + 4 = 9$

Can you explain why the total has gone up by $3$?