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Resources tagged with Prime factors similar to Weekly Problem 5 - 2007:

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Broad Topics > Numbers and the Number System > Prime factors

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Gaxinta

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Factoring Factorials

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Powerful Factorial

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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!?

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Thirty Six Exactly

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Flow Chart

Stage: 3 Challenge Level: Challenge Level:1

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

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One to Eight

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Just Repeat

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Great Granddad

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?


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