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14 Divisors

What is the smallest number with exactly 14 divisors?

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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.

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Oh! Hidden Inside?

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

Remainder

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the remainder of $2^{2002}\div 7?$

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What happens with different powers of $2$?

Try to explain the mathematics behind what you discover.