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:
Can you show that $1^{99} + 2^{99} + 3^{99} + 4^{99} + 5^{99}$ is divisible by $5$?