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More Mods

What is the units digit for the number 123^(456) ?

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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.

What Is the Question?

Stage: 3 and 4 Challenge Level: Challenge Level:1

Image 1
The answer is 49.

What is the question?

Why does it work?
Image 2
The answer is 42.

What is the question?

Why does it work?
Image 3
The answer is 63.

What is the question?

Why does it work?
Image 4
The answer is 56.

What is the question?

Why does it work?

Does this always work?
Can you extend the method to other numbers?