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WJEC MATHEMATICS
INTERMEDIATE
NUMBER
NUMBER PROPERTIES
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Contents
Odd and Even
Prime Numbers
Square Numbers
Cube Numbers
Triangular Numbers
Fibonacci Numbers
Factors
Multiples
LCM and HCF
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Odd and Even
Even numbers are numbers that end in a 0, 2, 4, 6, or 8
Odd numbers are numbers that end in a 1, 3, 5, 7, or 9.
Prime Numbers
Prime numbers are numbers that have only two factors; 1 and itself
(Another way of saying this is; Prime numbers are numbers that only
appear in their own times table)
NO!!
ONE IS
Here are the first few prime numbers.
2,3,5,7,11,13,17,19,23,29...
NOT A
PRIME
NUMBER!
Square Numbers
When you multiply a number by itself, you have squared it. The
result is known as a square number.
'Squared' is represented
by a power of 2
Learn the first 20 square numbers!!
e.g. 4×4 = 42
1,4,9,16,25,36,49,64,81,100,121,144,
169,196,225,256,289,324,361,400...
The inverse operation of 'squared' is 'square root'
So,
62 = 36 which means √36 = 6
132 = 169 which means √169 = 13
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Cube Numbers
Squaring a number means times by itself
Cubing a number means times by itself twice and is represented by a
power of 3
Example:
23 = 2×2×2 = 8
Here are the first few cube numbers.
1, 8, 27, 64, 225, 216, 343, 512...
Notice how the first, fourth, and fifth cube numbers are also square
numbers... How interesting.
The inverse operation of 'cubed' is 'cube root'
So,
3
43 = 64 which means √64 = 4
3
73 = 343 which means √343 = 7
Triangular Numbers
To help remember triangular numbers, think of 10 pin bowling.
As you can see, triangular numbers can be made visually into a
triangle. Also, you are adding one more onto the gap between each
term every time. You add 3, then add 4, then add 5, etc.
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Fibonacci Numbers
The Fibonacci series begins with 1, 1. Then every term is the sum of
the previous two terms.
Here are the first few Fibonacci numbers.
1, 1, 2, 3, 5, 8, 13, 21, 34...
Factors
If you can divide a number by 2, then 2 is a factor of that number.
If you can divide a number by 3, then 3 is a factor of that number.
etc.
The easiest way to work out factors is to find factor pairs. That is,
find all the pairs of numbers that multiply to give you the number.
Example 1
List all the factors of 12
The factor pairs are 12 & 1, 6 & 2, and 3 & 4.
So the factors of 12 are 1, 2, 3, 4, 6, 12
Example 2
List all the factors of 36
The factor pairs are 1 & 36, 2 & 18, 3 & 12, 4 & 9, 6 & 6
So the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Example 3
List all the factors of 19
The factor pairs are 1 & 19
Only two factors, one and itself!
IT'S PRIME!
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Multiples
The multiples of a number are that numbers' multiplication table.
So,
Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84,...
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 2.5 are 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, ...
Exercise N14
1. List all the factors of
a. 20
d. 25
b. 30
e. 26
c. 17
f. 38
g. 22
h. 50
i. 100
2. List the first 10 multiples of
a. 9
d. 24
b. 11
e. 31
c. 14
f. 17
g. 0.5
h. 7.2
i. 3.25
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Highest Common Factor
To find the highest common factor of two numbers, you need to work
out all factors of both numbers. The highest number that appears in
both lists is the HCF
Example 4
Find the HCF of 24 and 18
Factor pairs of 24 are 1&24, 2&12, 3&8, 4&6,
So factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factor pairs of 18 are 1&18, 2&9, 3&6,
So factors of 18 are 1, 2, 3, 6, 9, 18
There are a few numbers
that appear in both lists
(circled)
Remember, we want the
HIGHEST number in both
lists
HCF(24,18) = 6
Lowest Common Multiple
To find the lowest common multiple of two numbers, list both of their
times tables until you come across a number in both lists.
Example 5
Find the LCM of 12 and 9
Multiples of 12 are 12, 24, 36, ...
Multiples of 9 are 9, 18, 27, 36, ...
LCM(12,9) = 36
Note: This method of finding the HCF and LCM of two numbers only
works when the two numbers are relatively small. For larger
numbers, there is an alternative method. This can be found in the
booklet 'Product of Primes'.
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Exercise N15
1. Find the HCF of:
a. 12 and 20
b. 15 and 21
c. 30 and 70
d. 28 and 8
e. 105 and 120
f. 42 and 36
g. 30 and 54
h. 63 and 54
i. 12 and 24
2. Find the LCM of:
a. 6 and 7
b. 12 and 15
c. 25 and 20
d. 10 and 16
e. 12 and 24
f. 75 and 15
g. 28 and 30
h. 50 and 160
i. 1 and 2
Exam Questions N9
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8
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9
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