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Counting Factors

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


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.

Legs Eleven

Age 11 to 14 Challenge Level:

Imagine starting with the number $5238$.

We can write it as
                                  $5\times1000 + 2\times100 + 3\times10 + 8\times1$

Can you express the second number in the same way?

How many 5s, 2s, 3s and 8s are there when you combine the two numbers?