The prime factor mix-up in #MondayMaths

Blog: Vicki Robinson, Communications Officer

The prime factor mix-up in #MondayMaths

Posted: 12/09/16

Ready and energised for a new term? We’re teasing mathematical brains in #MondayMaths with this puzzle of problematic prime numbers.

Whether you’re tackling this in the staff room or with your students, we’re looking for two mystery numbers that have a highest common factor of 150 using all of their prime factors – (and we’re not telling you which prime factors belong to which)!

Our Year 8 students will learn about prime numbers, prime factorisation and highest common factors at the start of this term so this is a great way to get them thinking about what they’ve learned in a new context.

It’s always helpful to have another way to visualise a puzzle… this one’s a bit like dropping two vases, having them smash to pieces on the floor and trying to reconstruct the vases from the broken pieces. How do you begin to know which piece goes with which vase?

Multiple answers

The important thing to remind your students is that there is no one answer to this problem. Students will realise this fairly early on, once they’ve picked out the highest common factor from the jumble of primes.


In this picture, the prime factors that multiply to make 150 are highlighted in blue. Students should be looking to find these factors in the mix twice (one for each mystery number).

Across the curriculum

At the beginning of the Autumn term, Year 8 students will also be looking at Venn diagrams. This might be a nice way to reconstruct the prime factors in a way that represents both mystery numbers and their common factor.

Once they’ve found the prime factors of 150, students can then begin to reason that there are a number of solutions to the problem as they’re able to arrange the remaining factors between both numbers.

And here’s one last tip to pass on: 150 is the highest common factor and so the remaining factors should not be arranged in a way that contradicts this!

Look out for the answer on Twitter this Thursday – and get in touch to let us know whether this puzzle proves popular.