Download Factors and Primes

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NUMBER I
A
B
C
D
--I-"-h...- F'" ,r:l'("IRC'>·-7i,f · a nomb·e r are any numbers that divide Into It exactly.
PRIME NUMBER has exactly two factors. It can only be. divided by I and Itself.
84
a number IS a factor of another
number AND It Isa prime number then
It IS
..
ca~~e~ at:~~~Ep~~~~7a~o~~:use a
~
84 = 2 X 2 X 3
. = 2,'2 X 3 X 7~_..
Remember to circle
the prime fact"rs as ..-------
_ ~~~e~od;~:~~ ~a~ter. ....
.....
~
~2
8
('0
~® + _. _..._
Reniembe-'; to put In the multiplication signs.
15 callega. PROPUCT_of.E'RIME FACTOR5 . ~- .. __ ._.._..
. ThiS
.. _ - - - - -
The lowesf commonmultiple (LCMfOf t wo .
numbers _ls_the_LOWE5T NUMBER-that .ls a .
MULTIPLE of both numbers.
The highest common factor (HCF) of two
_J--I-rlurrlbers IS the HIGHE5T~NUMBERthat IS a FACTOR of both numbers.
--------------------------------------
~-
When draWing a factor tree, make sure you
t;continue until every branch ends with a prime
number. It doesn't matter which factor pairs
.. you choose for each branch. At the end, don't
~ forget to write out the product of primes.
Worked. example
(a) Express 108 as a product of its
prime factors.
108
Everything
In red IS
part of the
<::-----1--< answer.
~
o
Check ItI
54
~...I-
~
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f
9
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(b) Find the highest common factor (HCF)
of 108 and 24
1
!
~
"-.___.--"'--"--- . ..!'_~.~..-'_.__ ,
---
=
108 ./
_.- _. ...-. _ .._-_ .. - ...-...___-_..
---'
.... _ _
To find the HCF Circle all the pnme numbers
which are common to both products of
pnme factors. 2 appears tWice In both
products so you have to Circle It tWice.
Multiply the Circled numbers together to
~ find the HCF.
l L ------------_..,f
r· To find the LCM multiply the HCF by the
(c) Find the lowest common mUltiple (LCM)
of 108 and 24
LCM = 12 X 3 X 3 X 2 = 21G
-
.
~
108 = ® X ® X @ X 3 X 3
24. =®X®X 2 xC)
HCF IS 2 X 2 X 3 = 12
-- --- ----- -- -----
_
t
108 = 2 X 2 X 3 X 3 X 3 = 2 2 X 3 3
""'AM"._~""'_""'-
2 X 2 X3 X3 X3
numbers In both products that were not
Circled In part (b).
Alternatively, you can multiply 108 and 24
together and diVide by the HCF:
108 X 24 = 2592
2592 7 12 = 21G
...;;'- -
Now try this
(a) Express the following numbers as products
of their prime factors.
(i) 60
(ii) 96
(4 marks)
- -~-----------------.........
-
edexceli!5
(b) Find the highest common factor (HCF)
of 60 and 96
(1 mark)
(c) Work out the lowest common multiple
(LCM) of 60 and 96
(1 mark)
1