Rectangular Numbers


Most numbers can be arranged to make particular shapes. The factors of 8 are 2 × 4, so on a pegboard we arrange 8 pegs into 2 rows of 4.


1. a) What shape does this give us? b) Could it be arranged in any other way? If so, how?


2. Using a pegboard, geoboard or simply the squares in your copy, arrange these numbers into rectangular shapes by using their factors.


10 15 21 14 27 35


Numbers that have many factors can be arranged into more than 1 rectangular shape.


2 × 6 = 12 3 × 4 = 12


3. See how many different ways you can arrange the following numbers into rectangular shapes.


18 20 24 30 36 40 Puzzler


A set of football matches is to be organised in a round robin fashion: every participating team plays a match against every other team once and only once.


If 55 matches in total are played, how many teams participated? Square Numbers


Continue the sequence on your own pegboard. What do you notice about the shape of each of the numbers? We call each of these numbers square numbers.


Number Theory 2 101


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