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A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

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The number 12 = 2^2 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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Find the highest power of 11 that will divide into 1000! exactly.

Flow Chart

Age 11 to 14 Challenge Level:

Flow charts give very precise instructions, to perform a task or calculation.
The flow chart below uses three variables of which you can choose the starting value for M.

Select several values for M and try to establish what the flow chart does.
A printable version of the flow chart is available here

flow chart
If you start with certain numbers you reach the OUTPUT fairly quickly, but if you start with other numbers you don't.
e.g. if you start with 144 you reach the OUTPUT a lot sooner than if you start with 145.

What is special about the numbers that lead to an OUTPUT quickly?
What is special about the numbers that don't?

Certain values of D divide exactly into M during the procedure?
What is special about these values of D?

What is special about the value of N that you end up with?

How can the flow chart help you determine whether M is prime?