14 Divisors

What is the smallest number with exactly 14 divisors?

Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

What an Odd Fact(or)

Stage: 3 Challenge Level:

What can you say about the patterns in the last digits of powers of $2$, $3$, $4$ etc?

How can you use these patterns to say what the last digits are of the numbers raised to the power $99$?

Now can you say whether the sum is divisible by $5$?