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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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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.

Power Mad!

Age 11 to 14 Challenge Level:

What is the impact of the units digits on the product of two or more numbers?
e.g. what do you notice about the units digits in all the answers to the following:
2 x 3
42 x 53
652 x 43

What can you say about the patterns of the units digits of powers of 2, 3, 4, 5...?