Transcript Prime Factors

A number is a factor of another given number if the
given number can be EXACTLY divided by it
• e.g. 6 is a factor of 18 because 18 divided by 6 is 3
• Note that 3 is then also a factor of 18
A PRIME number is one which can be divided ONLY by
itself and 1
• It has two factors
• 1 is NOT a prime number – it has only 1 factor
All integers (whole numbers) other than 1 and prime
numbers, are called COMPOSITE numbers.
Composite numbers have more than 2 factors.
e.g. 6 is composite because it can be divided by 2 and 3
as well as 1 and 6 so the number 6 has four factors.
The factors of 6 are 1, 2, 3 and 6.
A list of the first 20 primes is:
2, 3, 5, 7,
11, 13, 17, 19,
23, 29,
31, 37,
41, 43, 47,
53, 59,
61, 67,
71, 73,
……
What is the next one?
To find the prime factorisation of 24:
• Since the first prime number is 2, see if 2 is a factor
of 24 by division
• It is, since 24 divided by 2 is exactly 12
• Now try to see if 2 is a factor of 12 – it is!
• So we have 24 = 2 x 12 = 2 x (2 x 6)
• Continue to divide the answer by 2 until it will not
divide exactly then move on to the next prime number
which is 3 etc until you get to 1
• Then 24 = 2 x 2 x 2 x 3 x 1
• Since 24 = 2 x 2 x 2 x 3 we have written 24
as a product of its prime factors
• In shorthand or index notation
• 24 is written as 23 × 3
• because there are 3 twos multiplied by one 3
• To use the TI-15 Explorer™ to
find the prime factors of a
number the calculator needs to
be set up in the following way:
– Press  button to enter the
Fraction Menu. The selection
U n/d n/d is displayed.
This lets you choose to
display fractions results as
mixed numbers (U n/d) or
improper fractions (n/d).
• Press the left and right 
arrow keys to move the
underline to choose the
display you want.
• In this case, move the
underline to n/d.
• Press the down arrow ,
and move the underline to
MAN. This lets you choose to
simplify fractions manually
(using the  key).
• Select .
Enter the fraction
• Press
(Remember the top line is the
numerator and the bottom line
is the denominator)
If
is visible at the top of the
screen then the fraction can be
simplified further.
Press . The simplified fraction is
displayed.
Press  and if, for example, a 2 is
shown, the fraction has been simplified
by dividing both the numerator and
denominator by 2. This tells you that 2
is a factor of 24.
If
is still visible, then further
simplification can occur.
Continue until you have recorded all
the prime numbers and your fraction is
now 1/1.
• You should have recorded that the fraction
24/24 became 12/12 then 6/6 then 3/3 then
1/1…
• The factors were 2, 2, 2 and 3
• So 24 = 2 x 2 x 2 x 3 = 23 × 3
• which is called the prime factorisation of 24
• To check if a number is a prime, check if any
of the prime numbers smaller than the square
root of that number are factors. If not then the
number is a prime.
• e.g. is 156 prime? – no, since it is an even
number and there is only one even prime –
that is 2!
• Is 157 prime? The square root of 157 is a bit
bigger than 12. Check if 2, 3, 5, 7, 11 are
factors of 157……….?