### Gaxinta

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

### Thirty Six Exactly

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

### Factoring Factorials

Find the highest power of 11 that will divide into 1000! exactly.

# Pairing Up

##### Stage: 3 Short Challenge Level:

The numbers $72, 8, 24, 10, 5, 45, 36, 15$ are grouped in pairs so that each pair has the same product. Which number is paired with $10$?

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If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.

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This problem is taken from the UKMT Mathematical Challenges.
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