Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.

Find the number which has 8 divisors, such that the product of the
divisors is 331776.

Method in Multiplying Madness?

Stage: 3 Challenge Level:

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...

If you had to work out $23 \times 21$ how would you do it?
What if you needed to work out $246 \times 34$?

Here are eight videos showing four different methods for working out the two multiplications. Can you make sense of them?

Grid Multiplication

$23 \times 21$

$246 \times 34$

Column Multiplication

$23 \times 21$

$246 \times 34$

Multiplying with Lines

$23 \times 21$

$246 \times 34$

Gelosia Multiplication

$23 \times 21$

$246 \times 34$

Once you have watched the videos, make up some multiplication calculations of your own and have a go at answering them using all four methods. Check that you get the same answer each time!

Here are some questions to consider:

Why does each method work?

What do the methods have in common?

What are the advantages and disadvantages to each method?

Extension challenge

Here is a video of another multiplication method, one where no writing down is needed along the way. Can you make sense of the video, and explain how this method works?