Multiples, Factors, and Prime Numbers
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By
Deepthi Menezes
1
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
3
A clock is set to ring at every 5
th
minute. Will it
ring 55 minutes later?
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.
5
13 x 1 =13
13 x 2 = 26
13 x 3 = 39
13 x 4 = 52
13 x 5 = 65
13, 26, 39, 52, 65
13, 26, 39, 52, 65
6, 12, 18, ____, ____
___, 6, 9, 12, ____, ____, 21
___, 24, 36, 48, 60, ____
Class 5-Multiples &Factors, LCM &HCF
6
24
30
3
15
18
12
72
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
10
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The factors of 12 are:
1 x 12
2 x 6
3 x 4
4 x 3
6 x 2
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
The factors of 48 are
1 x 48
2 x 24
3 x 16
4 x 12
6 x 8
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
15
60
The factor
pairs for 60
are
60=1x60
60=2x30
60=3x20
60=4x15
60=5x12
60=6x10
6
0
2
30
Composite
number
3
10
Composite
number
2
5
60 is written as the product of its prime factors
6
0
=
2
x
2
x
3
x
5
60=4x15
=2x2 x3 x5
The prime factors of 60 are
2
x
2
x
3
x
5
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
19
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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?
20
21
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.
•
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
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2
=
2
x
2
x
3
=
1
2
Uncommon
factors
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
Prime Factor Tree for 56
Prime Factor Tree for 48
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Look for common factors in both trees
Multiply them together =
8 is the biggest number that goes into both 56 and 48
So it is the Highest Common Factor
Finding the Highest Common Factor
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
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:
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
Explore the concept of multiples, factors, and prime numbers through examples and explanations. Learn how to identify multiples of a number, determine if a number is a multiple of another, distinguish between prime and composite numbers, and understand the properties of prime numbers. Gain insights into basic mathematical principles with practical illustrations.
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Presentation Transcript
By DeepthiMenezes 1
Multiples Multiplesof 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 12is a multiple of 3. Is 15 a multiple of 3? 3 x 5 = 15. So 15is 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, 26, 39, 52, 65 13, 26, 39, 52, 65 13 x 3 = 39 13 x 4 = 52 13 x 5 = 65 5
30 24 6, 12, 18, ____, ____ ___, 6, 9, 12, ____, ____, 21 3 15 18 ___, 24, 36, 48, 60, ____ 12 72 Class 5-Multiples &Factors, LCM &HCF 6
1 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2 3 4 5 6 7 8 9 10 100 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 2 x 6 3 x 4 4 x 3 6 x 2 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 6 x 8 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 60=1x60 60=2x30 60=3x20 60=4x15 60=5x12 60=6x10 30 2 2 15 3 5 15
60 The factor pairs for 60 are 60=1x60 60=2x30 60=3x20 60=4x15 60=5x12 60=6x10 Composite number 2 30 Composite number 3 10 5 2 60 is written as the product of its prime factors 60 = 2 x2 x 3 x 5
60=4x15 =2x2 x3 x5 60 4 15 2 2 3 5
60 30 The prime factors of 60 are 2 2 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. 3 5 15 5 1
Now let us try another example: 910 So 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 60 ,72 30 ,36 2 60 ,72 30 ,36 2 2 3 2 3 15 5 ,6 ,18 15 5 ,6 ,18 The common factors of 60 and 72 are 2 x 2 x 3 The HCF of 60 and 72 = 2x2x3=12 Uncommon factors
Factors of 60 Factors of 72
To find the LCM of 60 and 72 we multiply all the factors. 2x2 x3x5x6 = 336 60 ,72 2 30 ,36 2 15 ,18 3 5 ,6 So the HCF of 60 and 72 is 12 and LCM is 336
Prime Factor Tree for 56 Prime Factor Tree for 48 48 56 2 24 28 2 12 2 14 2 2 6 2 7 2 3 48 is the prime numbers 2 x 2 x 2 x 2 x 3 multiplied together 56 is all the prime numbers 2 x 2 x 2 x 7 multiplied together
Finding the Highest Common Factor 48 56 2 24 2 28 2 x 12 2 14 2 2 x 2 6 2 7 2 2 3 Look for common factors in both trees 8 Multiply them together = 8 is the biggest number that goes into both 56 and 48 So it is the Highest Common Factor
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 5 2 3 2 Write the other PRIME FACTORS of 700 in the 700 circle 3 5 7 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 60 ,72 30 ,36 2 2 5 2 3 2 3 2 3 5 15 5 ,6 ,18 7 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 2 24 28 2 x 2 12 2 14 2 x 2 2 6 2 7 3 2 8
