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Factors and Multiples

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by

Ivy Tan

on 17 September 2014

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Transcript of Factors and Multiples

Factors and Multiples
Factors and Multiples
Prime Numbers
Factors and Prime Factors
Member
(cc) photo by theaucitron on Flickr
12 X 12 = 12
= 144
Square and Square Root
Cube and Cube Root
A prime number is a natural number
greater than 1 that has no positive divisors other than 1 and itself.
Example: 2, 3, 5, 7, 11, 13, 17 etc
Composite Numbers
Numbers that can be written as a product of two or more prime numbers.

Example 4, 6, 8, 9, 10, 12, 14, 15 etc
Factors and Multiples
Factors
2 X 3 = 6
1 X 6 = 6
2 and 3 are factors of 6

Multiples
2, 4, 6, 8, 10 etc are multiples of 2
3, 6, 9, 12, 15 etc are multiples of 3

Note that 6 is the lowest common multiple between 2 and 3.
List all the factors of 12

1 X 12 = 12
2 X 6 = 12
3 X 4 = 12

1, 2, 3, 12, 6, 4 are factors of 12. There are 6 factors out of which 2 and 3 are prime factors.
Prime factorization of 12
12 = 2 X 2 X 3
= 2 X 3
2
A composite number can be written as a product of its prime factors. We call this prime factorization.
12
2
6
2
3
3
1
List the factors of 96
Prime Factorization of 96
96
2
48
2
24
2
12
2
6
2
3
3
1
1, 3, 6, 12, 24, 48, 96,
2, 4, 8,
16, 32.
96 = 2 X 2 X 2 X 2 X 2 X 3
= 2 X 3
5
144
= 12
2
12 X 12 X 12 = 12
3
1728
= 12
= 1728
2 X 3 X 2 X 3 X 2 X 3
= (2 X 3) X (2 X 3) X (2 X 3)
= (2 X 3)
3
2 X 2 X 2 X 3 X 3 X 3
= 2 X 3
=(2 X 3)
3
3
3
484
Find
by prime factorization
484
242
121
11
1
11
11
2
2
484
= 2 X 2 X 11 X 11
= 2 X 11
2
2
= (2 X 11)
2
484
= 2 X 11
= 22 (Answer)
= ((2 X 11)
2
Find the cube root of 1000 by prime factorization
1000
500
250
125
5
2
2
2
5
25
5
5
1
= 2 X 2 X 2 X 5 X 5 X 5
= 2 X 5
3
3
= (2 X 5)
3
1000
1000
=
(2 X 5)
3
= 2 x 5
= 10 (Answer)
1000
=
(2 X 5)
3
=
(2 X 5)
3
[
]
1
3
= 2 X 5
Note
3

X

1
3
Lowest Common Multiple
Greatest Common Factor
225, 750
75, 250
15, 50
3, 10
5
5
3
225, 750
75, 250
15, 50
3, 10
3
5
5
3
2
1, 10
1, 5
5
The GCF = 3 x 5 x 5
= 75
The LCM = 3 x 5 x 5 x 3 x 2 x 5
= 3 x 5 x 2
= 2, 250
2
3
1, 1
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