Download Prime Numbers

By
Deepthi Menezes
1
Multiples
Multiples of a number
can be made by
multiplying the number
by any whole number.
 1X12=12
 2X12 = 24
 3 X12 =36
 4X12=48
12, 24, 36, 48, 60, 72, 84,
96,108,120….are
multiples of 12

1 x 10 = 10,
2 x 10 = 20,
3 x 10 = 30,
4 x 10 = 40,
5 x 10 = 50,
6 x 10 = 60,
and so on ...
2

5
10
15
20
25
30
35
40
45
50
55
A clock is set to ring at every 5th minute. Will it
ring 55 minutes later?
3
Is 12 a multiple of 3?
If you multiply 3 by 4 you get 12, so 12 is a multiple
of 3.
 Is 15 a multiple of 3?
3 x 5 = 15. So 15 is a multiple of 3, (and also of 5).
 Is 21 a multiple of 6?
21 is not a multiple of 6 because you can't make 21
by multiplying 6 by any whole number.
6 x 3 = 18 and 6 x 4 = 24 but there is no whole
number between 3 and 4 that could give us an
answer of 21.

13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13, 26, 39, 52, 65
13, 26, 39, 52, 65
13 x 4 = 52
13 x 5 = 65
5
24
30
 6, 12, 18, ____, ____
15
18 21
3
 ___,
6, 9, 12, ____,
____,
 ___, 24, 36, 48, 60, ____
72
12
Class 5-Multiples &Factors, LCM &HCF
6
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
7
A prime number is a positive integer that has
exactly two positive integer factors, 1 and itself.
 For example, if we list the factors of 28, we have 1,
2, 4, 7, 14, and 28. That's six factors.
 If we list the factors of 29, we only have 1 and 29.
That's two factors. So we say that 29 is a prime
number, but 28 isn't.

8





A Composite Number can be divided evenly by numbers
other than 1 or itself.
Example: is 6 a Prime Number or Composite Number?
6 can be divided evenly by 2, or by 3, as well as by 1 or 6:
6=1×6
6=2×3
So 6 is a Composite Number
Class 5-Multiples &Factors, LCM &HCF
9


Factors are the numbers you multiply
together to get a product or a factor is a
number that exactly divides another number
without leaving a remainder.
12 can be written as the product of 2 x 6 or
2 x 6 = 12
2 and 6 are
the factors
of 12
12 is the
multiple of its
factors 2 and
6
10
The factors of 12 are:







1 x 12
2x6
3x4
4x3
6x2
12 x 1
12 can be divided evenly by 1, 2, 3, 4, 6 and 12:
 1 × 12 = 12
 2 × 6 = 12
 3 × 4 = 12

So 12 is a Composite Number

The factors of 12 are 1, 2, 3, 4, 6, and 12
11






For example, the product 24 has several
factors.
24 = 1 x 24
24 = 2 x 12
24 = 3 x 8
24 = 4 x 6
So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Class 5-Multiples &Factors, LCM &HCF
12








A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.
A number is divisible by 3 if the sum of the digits is
divisible by 3.
A number is divisible by 4 if the number formed by the
last two digits is divisible by 4.
A number is divisible by 5 if the last digit is either 0 or 5.
A number is divisible by 10 if the last digit is 0.
A number is divisible by 8 if the number formed by the
last three digits is divisible by 8.
A number is divisible by 9 if the sum of the digits is
divisible by 9.
A number is divisible by 6 if it is divisible by 2 AND it is
divisible by 3.
13
Writing facors
The factors of 48 are
1 x 48
2 x 24
3 x 16
4 x 12
6x8
Another way of writing factors is:
Write your first pair of factors with a
reasonable space between them, then
move on to the next pair until you have
them all.
This way, when you get to the 6,8 pair,
you can stop because 7 is not a factor
and you already have 8 in your list.
14

60=1x60
60=2x30
60=3x20
60=4x15
60=5x12
60=6x10
60
30
2
2
15
3
5
15


The factor
pairs for 60
are
60=1x60
60=2x30
60=3x20
60=4x15
60=5x12
60=6x10
60
Composite
number
2
30
Composite
number
3
10
2
5
60 is written as the product of its prime factors
60 = 2 x2 x 3 x 5

60=4x15
=2x2 x3 x5
60
4
2
15
2
3
5
2 60
2 30
3 15
5 5
1
The prime factors of 60 are
2x2x3x5
2, 3, and 5 are all prime numbers,
so we have prime factored 60. All
we have to do now is neaten our
answer up a bit. It is customary to
write prime factorizations in
increasing order, that is with the
smallest numbers first.

Now let us try another example: 910
So the prime factorization of 910 is 2x5x7x13
19

A cold drink truck visits Rita's neighbourhood every 4
days and Amul ice cream truck visits her
neighborhood every 5 days. For the month of June on
which day will both the trucks visit on the same day?
1
8
15
22
29
2
9
16
23
30
3
10
17
24
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
20
In the given problem we have to first find the multiples of both
the numbers.
 Cross out the multiples that are common. (20 and 40)
 Which multiple is the least-20
 Both the trucks will visit the neighbour hood on 20 June or
after 20 days.

Truck
Days of visit
1
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,...
2
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,...
21
Multiples of 18 18, 36, 54, 72, 90, 108, 126, 144,…
Multiples of 24 24, 48, 72, 96, 120,144, ….
•
•
•
Common multiples of 18 and 24 are 72 and 144
The least common multiple of 18 and 24 is 72.
LCM = 72
Find the HCF of 60 and 72
2
60 ,72
2 30 ,36
3
15 ,18
5 ,6
The common factors of 60
and 72 are 2 x 2 x 3
The HCF of 60 and 72 =
2x2x3=12
2
60 ,72
2 30 ,36
3
15 ,18
5 ,6
Uncommon
factors
Factors of
60
Factors of
72




To find the LCM of
60 and 72 we
multiply all the
factors.
2x2 x3x5x6 = 336
So the HCF of 60
and 72 is 12 and
LCM is 336
2
60 ,72
2 30 ,36
3
15 ,18
5 ,6
 Prime Factor Tree for 56

Prime Factor Tree for 48
48
56
2
28
2
24
12
2
14
2
2
2
7
56 is all the prime numbers
2 x 2 x 2 x 7 multiplied
together
6
2
3
48 is the prime numbers
2 x 2 x 2 x 2 x3
multiplied together
Finding the Highest Common Factor
48
56
2
28
2
x
14
2
2
12
2
2
7
24
2
x
2
2
Look for common factors in both trees
Multiply them together =
8
6
2
8 is the biggest number that goes into both 56 and 48
So it is the Highest Common Factor
3
The prime factors of :
56 = 2 x 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
The prime numbers that are common are:
2x2x 2= 8
So the HCF of 56 and 48 is 8

Write the common prime
factors of both 504 and
700 here .
The HCF =2X 2 X 7=28
504 = 2 x 2 x 2 x 3 x 3 x 7
700 = 2 x 2 x 5 x 5 x 7
504
700
2
3
3
5
2 2
7
5
Write the other PRIME
FACTORS of 700 in the
700 circle
Write the other PRIME
FACTORS of 504 in the
504 circle
The LCM is found by multiplying all the numbers from the circles
504
700
3
3
5
2 2
7
60 ,72
2
2
2 30 ,36
5
15 ,18
5 ,6
3
48
56
The prime factors of :
56 = 2 x 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
The prime numbers that are common are:
2x2x 2= 8
So the HCF of 56 and 48 is 8
2
28
2
x2
14
2
2
2
7
24
12
2
x2
2
6
2
8
3