### 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?

##### Age 11 to 14 Challenge Level:

Take a look at the two multiplications below. What do you notice?

$32 \times 46 = 1472$
$23 \times 64 = 1472$

The digits in this multiplication have been reversed, and the answer has stayed the same!

Is this surprising? Can you find other examples where this happens?

What do you notice about the pairs of two digit numbers that produce this special result?