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Resources tagged with Prime factors similar to Some Cubes:

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Broad Topics > Numbers and the Number System > Prime factors

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Some Cubes

Stage: 5 Challenge Level: Challenge Level:1

The sum of the cubes of two numbers is 7163. What are these numbers?

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Public Key Cryptography

Stage: 5

An introduction to the ideas of public key cryptography using small numbers to explain the process. In practice the numbers used are too large to factorise in a reasonable time.

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Different by One

Stage: 4 Challenge Level: Challenge Level:1

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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Em'power'ed

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

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There's Always One Isn't There

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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A Biggy

Stage: 4 Challenge Level: Challenge Level:1

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

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Factoring a Million

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

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Fac-finding

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

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Can it Be

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

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Rarity

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Show that it is rare for a ratio of ratios to be rational.

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Why 24?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

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Factorial Fun

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many divisors does factorial n (n!) have?


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