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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.


Age 7 to 14 Challenge Level:

You may find the article on Divisibility Tests helpful.

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
In the interactivity below, the computer generates two random digits.
Your task is to find the largest possible three-digit number which uses the computer's digits, and one of your own, to make a multiple of 2, 3, 4 or 6.

Can you decribe a strategy that ensures your first 'guess' is always correct?

Enter the biggest three-digit multiple of you can think of that uses the digits:

Something else to think about:
What is the largest possible five-digit number
divisible by $12$ that you can make from the digits
$1$, $3$, $4$, $5$ and one more digit? 
Click here for a poster of this problem.