Primes, Factors & Multiples – Demonstration
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Check animations and delete slides not needed for your class.
How many ways can you complete these
calculations using integers (whole numbers).
×
= 12
1 × 12
2×6
3×4
×
1 × 30
2 × 15
3 × 10
5×6
×
= 20
1 × 20
2 × 10
4×5
= 30
×
1 × 36
2 × 18
3 × 12
4×9
6×6
= 36
×
1 × 12
2×6
3×4
×
1 × 30
2 × 15
3 × 10
5×6
= 12
These numbers are
the factors of 12.
= 30
These numbers are
the factors of 30.
×
1 × 20
2 × 10
4×5
×
1 × 36
2 × 18
3 × 12
4×9
6×6
= 20
These numbers are
the factors of 20.
= 36
These numbers are
the factors of 36.
A factor is an integer number that can make other numbers.
‘factory’
What numbers can 6 make?
6
6
12
18
24
6 is a factor of an
infinite amount
of numbers!
Think about the reverse.
What factors can make 12?
1
2
3
4
6
12
12
A factor is an integer number that can make other numbers.
Think about the reverse.
What factors can make 24?
1
2
3
4
24
24
12
8
6
How have the factors been arranged?
DEMO
Factors
Find the factors of 10.
1 × 10
2 × 5
3
4
Can we go any higher?
1, 10, 2, 5
DEMO
Factors
Find the factors of 20.
1 × 20
2 × 10
3
4 × 5
Can we go any higher?
1, 20, 2, 10, 4, 5
DEMO
Factors
Find the factors of 35.
1 × 35
2
3
4
5 × 7
6
Can we go any higher?
1, 35, 5, 7
DEMO
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Can we go any higher?
1, 15, 3, 5
DEMO
YOUR TURN
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Find the factors of 14.
1 × 14
2 × 7
3
4
5
6
Can we go any higher?
1, 15, 3, 5
1, 14, 2, 7
DEMO
YOUR TURN
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Find the factors of 30.
1
2
3
4
5
× 20
× 15
× 10
× 6
Can we go any higher?
1, 15, 3, 5
1, 20, 2, 15, 3, 10, 5, 6
DEMO
YOUR TURN
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Can we go any higher?
1, 15, 3, 5
Find the factors of 32.
1 × 32
2 × 16
3
4 × 8
5
6
7
1, 32, 2, 16, 4, 8
DEMO
YOUR TURN
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Find the factors of 25.
1 × 25
2
3
4
5 × 5
Can we go any higher?
1, 15, 3, 5
1, 25, 5
DEMO
YOUR TURN
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Find the factors of 36.
1
2
3
4
5
6
×
×
×
×
36
18
12
9
× 6
Can we go any higher?
1, 15, 3, 5
1, 36, 2, 18, 3, 12, 4, 9, 6
DEMO
Factors
Find the factors of 15.
1 × 15
2
3 × 5
4
Can we go any higher?
1, 15, 3, 5
YOUR TURN
1) Find all the factors of these numbers.
a)
14: 1, 14, 2, 7
b)
18: 1, 18, 2, 9, 3, 6
c)
26: 1, 26, 2, 13
d)
17: 1, 17
e)
40: 1, 40, 2, 20, 4, 10, 5, 8
f)
49: 1, 49, 7
g)
48: 1, 48, 2, 24, 3, 16, 4, 12, 6, 8
h)
100: 1, 100, 2, 50, 4, 25, 5, 20, 10
i)
61: 1, 61
List the factors for each of these numbers.
16
7
4
11
9
13
25
14
1, 16, 2, 8, 4
1, 7
1, 2, 4
1, 11
1, 9, 3
1, 13
1, 25, 5
1, 14, 2, 7
How could we categorise these numbers according
to their factors (put them into groups)?
Numbers with two factors:
Prime numbers
Numbers with an odd amount of factors:
Square numbers
7
11 13
16
4
9
25
A prime number is a number that has exactly 2 factors.
7
14
1, 7
1, 14, 2, 7
Prime
Non-Prime
Prime numbers are the building blocks for all numbers because
every number has at least one prime factor.
Large prime numbers are very difficult to find, this makes them
useful for encryption like in banking and online messaging.
For 1 to 50, how many prime numbers are there?
Start at 1 and work up.
Can you develop a method?
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
How can we find prime numbers?
Instead of finding prime numbers,
we can do the reverse: eliminate non-prime numbers.
We know multiples of 2 can’t be prime…
so we can eliminate them (but not 2!)
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
Prime numbers from 1 to 100
2, 3, 5, 7, 11, 13, 17, 19,
23, 29, 31, 37, 41, 43,
47, 53, 59, 61, 67, 71,
73, 79, 83, 89 & 97
Multiples
A multiple is a number that is made by multiplying a factor.
The multiples of 3 : 3, 6, 9, 12, 15, 18…
The multiples of 7 : 7, 14, 21, 28, 35, 42…
The multiples of 13 : 13, 26, 39, 52…
Multiples
A multiple is a number that is made by multiplying a factor.
Which number is a multiple of 4?
6
12
14
Which of these numbers is a multiple of 5?
60
54
24
15
28
Which of these numbers is a multiple of 8?
56
20
96
22
24
Is zero a multiple of 4?
44
32
Multiples
List the first 5 multiples of 6 :
6, 12, 18, 24, 30
List the first 8 multiples of 4 :
4, 8, 12, 16, 20, 24, 28, 32
List the first 7 multiples of 9 :
9, 18, 27, 36, 45, 54, 63
What is the 3rd multiple of 11?
33
What is the 5th multiple of 7?
35
What is the 7th multiple of 12?
84
13 16
4
36 24 22 12
1
6
7
42 20
14 31
33
5
9
12 15
8
Which numbers are…
Factors of 20?
1
4
Factors of 26?
1
13
Factors of 40?
1
4
8
20
5
5
20 Prime?
5
7
13
Multiples of 5? 5
15
20
Multiples of 7? 7
14
42
31
Questions?
Comments?
Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to email:
tom@goteachmaths.co.uk