### Thirty Six Exactly

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

### Even So

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

### Power Crazy

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?

# Powerful Zeros

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Imagine the number $3^4\times 4^5\times 5^6$ is written out in full. How many zeros are there at the end of the number?
Â
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Â Â

This problem is taken from the UKMT Mathematical Challenges.