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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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Summing Consecutive Numbers

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

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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?

Power Crazy

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
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What can you say about the values of n that make 7 n + 3 n a multiple of 10?

Are there other pairs of integers between 1 and 10 which have similar properties?