Find The Factors – the blog of Iva Sallay

One of the blogs I follow is Find The Factors.  It’s very different from this one.  For a start, it’s frighteningly efficient, and appears on a daily basis – not like this one, which happens now and again when I get around to it.

Iva Sallay gives us a new puzzle every day, where you’re given a few entries in a multiplication square and have to figure out the multipliers heading the columns and rows.  So clearly we’re in an area highlighting multiplication facts – in the puzzle below the 42 in the top row has to be the product of 6 and 7 – but we can’t immediately do anything with this because we don’t know if  it the 42 comes from 6×7 or 7×6.  And the 20 will offer more problems, since we’ll have to discover whether it comes from the product of 2 and 10, or 4 and 5; even then, we must decide on the orientation.

A Find The Factors puzzle will be full of challenges like this, and the beauty of the blog is that they’re graded from level 1 all the way to the most challenging level 6.  The puzzle below is level 4:



This puzzle is number 177, and you’ll usually get some facts about the puzzle number – its factorisation, and in this case, you’re also given a magic square made up of prime numbers; the magic total is 177.

The obvious comparison is to Sudoku puzzles.  I rarely do Sudoku; I usually find I get so far and then have no option other than guessing between several possibilities until I find the right one.  Just occasionally I’ve had to do this with Find The Factors, but generally speaking even at level 6 I can eventually reason the whole thing out.  Mind you, sometimes I have to work hard, but that’s surely the whole idea!

I’ve shown one of Iva’s 1-12 puzzles, but she also gives 1-10 puzzles as well, and you can have a week’s worth of puzzles to download in Excel format.

You can find Iva’s blog at


I do the puzzles for my own enjoyment, but my pupils would find them daunting and indeed too time-consuming.  However, the basic idea is one I’m happy to challenge them with, so I may offer them a 4×4 square constructed on the same theme.  Once they’d tackled one of those, we’re likely to use the interactive version on the NRICH website  (  where you can find a variety of challenges all based on the same starting point).



3 responses

  1. Thank you for the great write-up.
    I do have puzzles that would be just right for students who have barely learned how to divide. Look under Level 1 at for the excel file called Division Facts Puzzles to find puzzles where each number from 1 to 12 is the common factor of its own puzzle. If you tell the students what the common factor is, that puzzle will be easier for them to solve.

    1. A pleasure. I really admire your commitment and discipline to produce a puzzle every day!

  2. […] It’s been a busy summer for me and lots of other people, yet Alan Parr found the time this summer to write a great post about the Find the Factors puzzles.  You can read it at established1962 find-the-factors. […]

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