# One to Eight

Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.

## Problem

Here are some 'funny factorisations'. Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits $2$ to $9$ once and only once.

** $\times$ ** $= 4876$

** $\times$ ** $= 5394$

Now do the same with the digits $1$ to $8$ to complete the
following expressions.

** $\times$ ** $= 1368$

$5$* $\times$ $6$* $=$ ****

$52$ $\times$ ** $=$ ****

## Getting Started

Expressing the four digit numbers as the product of their prime factors may help you narrow down the options.

The units digit of the factors will determine the units digit of the product.

## Student Solutions

Sue from CBEC Basingstoke sent the following explanation to the first question:

** X ** = 4876If you write 4876 as a product of prime factors you get 2 x 2 x 23 x 53

From this you need to find two, two digit numbers that use the digits 2, 3, 5 and 9

This has to be 2 x 2 x 23 = 92 and 53

We also received correct solutions from Jenny, Greenian, Rachael, Jacqui and Sam, from The Mount School, and Debbie from Forres Academy. Well done to you all.

53 x 92 = 4876

62 x 87 = 5394

24 x 57 = 1368

58 x 64 = 3712

52 x 34 = 1768

We'd like to hear from anyone who would like
to explain how they solved these problems.

We are always interested in the reasoning that has helped you reach
your solutions.

## Teachers' Resources

A problem in which students can apply their understanding of how prime numbers form the building blocks of numbers.

Students will need to develop strategies that help them narrow down their options and then work systematically.

You can find a similar problem on the NRICH site: Funny Factorisation