### Counting Factors

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

### 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?

### 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?