products of primes

the powerpoint is here
[ it needs to be downloaded for the animations to work ]

what is the common form of these pairs of numbers?

what, in general, will the hcf be?

the lcm?

prime number images

an interesting prime numbers graphic

shows the sum of the factors (listing all the factors in the sum) and the aliquot sum
tells you whether a number is abundant, deficient or perfect (or prime)
the chart can be dragged across to the left (see what happens at 360)

I have mentioned elsewhere my enthusiasm for using Alec McEachran's 'Primitives' application (that can be viewed full screen)

this screenshot shows the numbers 45, 46, 47 and (just) 48

composite numbers being shown in an interesting form











another representation shows the numbers on a grid, with the prime factorisation indicated by sectors

factor trees

nudging towards the fundamental theorem of arithmetic
(and maybe to provide a reason why 1 is not considered to be a prime number any longer)
this can be done with or without this sheet
[e.g. pose the task of finding all the ways that 90 can be broken down]

what are the missing products?

factor trees drawn by students in Y5 at the International School of Toulouse
see pinkmathematics

what are the missing numbers?



















find a way to break down 720 into a product of prime factors that fits this tree:

the product product

4321

what is the remainder when 4321 is divided by:
2? 3? 4? 5? 6? (not 7) 8? 9? 10?
why is this?



what is the smallest number that has this property?