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Flow Chart

Age 11 to 14
Challenge Level Yellow star
  • Problem
  • Getting Started
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Vivek from UWCSEA showed a very clear understanding of what the flow chart does:

The numbers that lead to an output quickly have very small prime factors.
The numbers that don't, have very large prime factors.

The values of D that divide exactly into M are all prime numbers.

The value of N is the number of prime factors that the number has (e.g. 12 can be expressed as the product of 3 prime factors - 2 x 2 x 3 and the output when M = 12 is 3).

The flow chart helps you determine whether M is prime because if M is prime, the output is always 1: M can only be divided by D when D is the prime number itself. This makes it go around in a continuous loop without adding anything to N until M is divided by D (which equals to M), so N is always 1 when M is prime.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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