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Broad Topics >

Numbers and the Number System > Prime factors

##### Age 11 to 14 Challenge Level:

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?

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.

##### Age 11 to 14 Challenge Level:

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

The flow chart requires two numbers, M and N. Select several values
for M and try to establish what the flow chart does.

##### Age 11 to 14 Challenge Level:

Think of any three-digit number. Repeat the digits. The 6-digit
number that you end up with is divisible by 91. Is this a
coincidence?

##### Age 11 to 14 Challenge Level:

Great Granddad is very proud of his telegram from the Queen
congratulating him on his hundredth birthday and he has friends who
are even older than he is... When was he born?