Understanding Sieve of Eratosthenes Video Lecture - & Pedagogy Paper 2

I have had several requests to show the
workings of the sieve of eratosthenes so
here goes
it's an ancient Greek method of finding
prime numbers in an array or the
hundreds chart it was created by
Eratosthenes one of those Greek
mathematicians from way back we can use
this to identify prime numbers up to 100
the following steps will help us find
the prime numbers start by crossing out
the number 1 do you know why we cross
out the number 1
any takers well it's because a problem
number is any number greater than one
and only divisible by itself and one so
one cannot be a prime number because it
is not greater than one okay now let's
put a circle around the number two it is
prime number because it is greater than
one and is only divisible by itself and
one two is also the only even prime
number next we'll cross out all
multiples of 2 to find the multiples of
two simply skip count by two for example
2 4 6 8 10 and so on
did you notice any patterns for the
multiples of two you do realize I can't
hear you they all end in two four six
eight or zero so if a number ends in two
four six eight or zero then one of its
factors is two next let's put a circle
around three it's a prime number because
it is greater than one and it's only
divisible by itself and one next we'll
want to cross out all the multiples of
three to find the multiples of three you
can skip count by three for example
three six nine twelve fifteen and so on
you'll notice four is already crossed
out that's because it's already a
multiple of the prime number to the next
unmarked number is five I'll just play
Circle around five because it is a prime
number next let's skip count by fives do
you notice any patterns in the multiples
of five
I sure hope someone got that they all
end in 5 or 0 so if a number ends and 5
or 0 you know one of its factors is 5 6
is not a prime number do you know why
because six has more than two factors
its factors are one six two and three
all the multiples of six are already
crossed out because if a number is a
multiple of six it already had factors
of two and three looking at the table
our next unmarked number is seven it is
prime because it is greater than one and
only has one and itself as factors will
circle it and then proceed to markets
multiples most of sevens multiples are
already crossed out because those
multiples have more than two factors
eight is not a prime number do you know
why
because eight has more than two factors
the factors of 8 are one eight four and
two eighths multiples are already
crossed out because if a number is a
multiple of eight it also has a factor
of two nine is not a prime number
because as factors are one nine and
three it has more than two factors all
the multiples of nine have also been
crossed out because they have other
factors sides nine for example 18 has
already crossed out because it has
factors of 1 2 3 6 9 and 18 10 is not a
prime number because it has factors of 1
2 5 and 10 all the multiples of 2 and 5
have already been crossed out this also
means that all of the multiples of 10
have been crossed up now that we found
all the multiples of 2 through 10 all we
have left that are not circled or prime
numbers why are they prime numbers
remember because they only have factors
of 1 and themselves our prime numbers
between 2 and 100 are 2 3 5 7 11 13 17
19 23 29 31 37 41 43 47 53 59 61 67 71
73 79 80 389 and 97 so remember in order
to find a number that is not prime try
to see if it is a multiple of another
number and as always the sieve of
eratosthenes is your safety net for
prime numbers
uh-oh I need a vacation