Transcript mathspresentationpowerpoint1

Factors and
Multiples
What
are prime numbers?
If a number has only two
different factors, 1 and itself,
then the number is said to
be prime.
For example, 7 = 7 x 1
7 is a prime number since it has only two
different factors.
Clearly, 2 = 1 x 2
3=1x3
5=1x5
7=1x7
11 = 1 x 11
Therefore 2, 3, 5, 7, 11… are all prime
numbers.
What
are composite numbers?
A number that has more
than two factors is called
a composite number.
For example, 14 = 1 x 14 and 2 x 7
So, 14 is a composite number as it
has more than two factors.

State which of the following
numbers are prime:
46
b) 19
a)

46 is not a prime because 46
= 2 x 23.

19 is a prime since it has only
two different factors, 1 and
19.
‘Factors’ are the numbers
you multiply to get
another number:
2x3=6
Factor
Factor
 Explain
your reasoning or give a counter
example to answer
• If a number is divisible by 3, is it divisible by 9?
• If a number is divisible by 9, is it divisible by 3?
 Which
of the following numbers are
divisible by 4?

Determine the remainder when the number is
divided by 4?
• 14,710,816,558
• 4,328,104,292
 The
first 10 prime numbers are 2, 3, 5, 7,
11, 13, 17, 19, 23 and 29.
• Which of these prime numbers would you have to
consider as possible factors of 367 in order to
determine whether 367 is a prime or composite
number?
• Is 367 prime or composite?
 Which
of the following numbers are prime?
• 231
• 277
• 683
To test if a number is prime or
composite by hand, the easiest
thing to do is test if its divisible
by prime numbers. If none of
them divide it, once the numbers
you’re dividing by get bigger than
the square root of the number
you’re testing, you’re done and
know it’s prime.
For example, here’s how you would test
if 107 is prime:
 It’s
odd, so it’s not divisible by 2;
 It’s not divisible by 3 (use the divisibility rule: 1 + 0
+ 7 = 8, not 3 or 6 or 9)
 It’s
not divisible by 5 (doesn’t end in 5 or zero)
 It’s not divisible by 7 (if it were, 107 – 7 = 100
would be divisible by 7, which we know isn’t true)
 At
this point, we know it’s not prime, since
we’d need to check 11 next. But 11 x 11 =
121, bigger than 107, so 11 is less than the
square root of 107.
INTERACTIVE SITE FOR PRIMES AND
COMPOSITES
http://www.321know.com/fra63ax2.htm
Sieve of Eratosthenes
A prime number is a whole number that has exactly two factors, 1 and
itself.
We can use the Sieve of Eratosthenes to find out whether a number is
prime or composite.








The following example illustrates how the Sieve of Eratosthenes, can
be used to find all the prime numbers that are less than 100.
Step 1: Write the numbers 1 to 100 in ten rows.
Step 2: Cross out 1 because 1 is not a prime.
Step 3: Circle 2 and cross out all multiples of 2. (2, 4, 6, 8, 10, ...)
Step 4: Circle 3 and cross out all multiples of 3. (3, 6, 9, 12, 15, ...)
Step 5: Circle 5 and cross out all multiples of 5. (5, 10, 15, 20, ...)
Step 6: Circle 7 and cross out all multiples of 7. (7, 14, 21, 28, ...)
Circle all the numbers that are not crossed out and they are the
prime numbers less than 100.