Gaxinta

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?

Thirty Six Exactly

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

Factoring Factorials

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

Flow Chart

Stage: 3 Challenge Level:

Why do this problem?

This problem is about flow charts, factors and prime factorisation.

Possible approach

Teachers can present the flow chart to students and ask them to try to figure out what to do with it. A table of values can be drawn on the board to collect results.

There won't be an obvious algebraic relationship emerging but this might be a good opportunity to emphasise the need to look at the underlying mathematics rather than just the values. Discussion with the group can draw out comments and observations about what the flow chart is doing.

Students can then be directed to the questions in the problem.

If the group hasn't had much experience of using flow charts, some time could be set aside to discuss the merits of flow charts (efficient, clear, unambiguous) and some of their drawbacks (repetitive, tedious - try starting with a large prime number!).

Possible extension

Students can be asked to produce a flow chart that finds the Highest Common Factor or Lowest Common Multiple of two inputs. Half the class could work on the HCF while the other half works on the LCM. They could then swap and test each other's flow charts.

Possible support

Suggest to students that they use a table of values to keep track of M, D and N as they change.

Factors and multiples. Modulus arithmetic. Divisibility. Multiplication & division. Place value. Factorials. Prime factors. Logic. smartphone. Mathematical reasoning & proof.

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