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An Advanced Mathematics Lesson Starter Of The Day

The following challenge appeared in Mathematical Pie, a Mathematical Association publication.

The prime factorisation of 600 is 2³ x 5² x 3. We can make all the factors of 600 by choosing from four possibilities for the 2 (to include it 0, 1, 2 or 3 times); three possibilities for the 5 (to include it 0, I or 2 times) and two possibilities for the 3 (to include it or not).

Altogether 4 x 3 x 2 = 24 possibilities (if we don't choose any of the three this will give the factor l). So 600 has 24 factors.

Can you use the same idea to find all the numbers below 1000 which have exactly 20 factors?

Number Factory

Extension

The following challenge appeared in the book Math Girls by Hiroshi Yuki.

"Describe a method for summing the divisors
of a given positive integer n"

Starter of The Day Transum Mathematics Topics

Topics: Starter

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Answer

More Advanced Lesson Starters

More Mathematics Lesson Starters

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