Download Factors, Divisibility, & Prime / Composite numbers

Lesson 1d
Factors, Divisibility, &
Prime / Composite numbers
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Factors & Divisibility
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Definition:
A number is divisible by another
number if, when you divide, the
remainder is 0.
3
8 24
24
0
24 is divisible
by 8.
2
9 24
18
6
24 is not
divisible by 9.
Since 24 is divisible by 8, 8 is called a factor of 24.
Here are all the factors of 24.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors & Divisibility cont. . .
The number 24 is a multiple of
each of its factors.
4 • 6 = 24, 2 • 12 = 24, 3 • 8 = 24, 1 • 24 = 24
Multiples of 2 are:
Multiples of 3 are:
Multiples
Multiples
Multiples
Multiples
Multiples
of
of
of
of
of
4 are:
6 are:
8 are:
12 are:
24 are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,
24, 26, 28, 30, . . .
3, 6, 9, 12, 15, 18, 21, 24, 27, 30,
33, 36, . . .
4, 8, 12, 16, 20, 24, 28, . . .
6, 12, 18, 24, 30, 36, 40, . . .
8, 16, 24, 32, 40, 48, 56, . . .
12, 24, 36, 48, . . .
24, 48, 72, . . .
Next
Factors & Divisibility cont. . .
Thus, divisible by, factor of, and
multiple of are related terms.
4 • 6 = 24, 8 • 3 = 24, 12 • 2 = 24, 1 • 24 = 24
24 is divisible by 8.
8 is a factor of 24.
24 is a multiple of 8.
Next
Next
Example 1
Choose True or False for each
sentence.
(a) 12 is a factor of 60.
True or False?
(b) 25 is a factor of 60.
True or False?
(c) 19 is divisible by 8.
True or False?
(d) 30 is divisible by 15.
True or False?
(e) 12 is a multiple of 12. True or False?
(f) 36 is a multiple of 9.
True or False?
Answer A is True because :
12 • 5 = 60
Answer B is False because :
2
25 60
50
10
25 is not a
factor of 60.
Answer C is False because :
2
8 19
16
2
19 is not
divisible by 8.
Answer D is True because :
2
15 30
30
0
30 is divisible
by 15.
Answer E is True because :
12 • 1 = 12
12 is a multiple
of 12.
Answer F is True because :
9 • 4 = 36
36 is a multiple
of 9.
Example 2
List all the factors of 15.

List all the numbers through 15.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ,13, 14, 15

Divide 15 by each number in the list.
Reject each divisor that produces a
nonzero remainder.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ,13, 14, 15
Answer: 1, 3, 5, 15
Your Turn
On a piece of paper, list all the
factors of 9.
Click here to check your answer
The Process

List all the numbers through 9.
1, 2, 3, 4, 5, 6, 7, 8, 9

Divide 9 by each number in the list.
Reject each divisor that produces a
nonzero remainder.
1, 2, 3, 4, 5, 6, 7, 8, 9
Answer: 1, 3, 9
Your Turn
On a piece of paper, list all the
factors of 22.
Click here to check your answer
The Process

List all the numbers through 22.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 , 15, 16, 17, 18, 19, 20, 21, 22

Divide 22 by each number in the list.
Reject each divisor that produces a
nonzero remainder.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 , 15, 16, 17, 18, 19, 20, 21, 22
Answer: 1, 2, 11, 22
Your Turn
On a piece of paper, list all the
factors of 5.
Click here to check your answer
The Process


List all the numbers through 5.
1, 2, 3, 4, 5
Divide 5 by each number in the list.
Reject each divisor that produces a
nonzero remainder.
1, 2, 3, 4, 5
Answer: 1, 5
This is a prime number which we’ll discuss later in the lesson
Divisibility Tests are shortcuts for finding
factors of whole numbers.
Here are six useful divisibility tests:
1. A number is divisible by 2 if the last digit is an even number.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 4 if the last 2 digits name a multiple of 4.
4. A number is divisible by 5 if the last digit is 0 or 5.
5. A number is divisible by 9 if the sum of its digits is divisible by 9.
6. A number is divisible by 10 if the last digit is 0.
Click the text for Examples
A number is divisible by 3 if the sum of its
digits is divisible by 3.
Examples:
411  4 + 1 + 1 = 6
9,855  9 +8 + 5 + 5 = 27  2 + 7 = 9
A number is divisible by 4 if the last 2 digits
name a multiple of 4.
Examples:
1036  36 = 4 • 9
Since 36 is divisible by 4, 1036 is also!
A number is divisible by 5 if the last digit is 0
or 5.
Examples:
10, 25, 40, or 75 are all divisible by 5
because the last digit is a 0 or a 5
A number is divisible by 9 if the sum of its
digits is divisible by 9.
Examples:
153 1 + 5 + 3 = 9  9 is divisible by itself.
468 4 +6 + 8 = 18  9 • 2 = 18
Since 18 is divisible by 9 then 468
is also!
A number is divisible by 10 if the last digit is 0.
Examples:
10, 20,40, 70, 110, 2190 are all divisible
by 10 because the last digit is a 0.
Practice
Which of these numbers are divisible
by four?
116
Yes
2028
Yes
Click here to review the
shortcuts again
1114
No
Practice
Which of these numbers are divisible
by three?
51
Yes
39
Yes
Click here to review the
shortcuts again
82
No
Divisibility Tests are shortcuts for finding
factors of whole numbers.
Here are six useful divisibility tests:
1. A number is divisible by 2 if the last digit is an even number.
2. A number is divisible by 3 if the sum of its digits is divisible by 3.
3. A number is divisible by 4 if the last 2 digits name a multiple of 4.
4. A number is divisible by 5 if the last digit is 0 or 5.
5. A number is divisible by 9 if the sum of its digits is divisible by 9.
6. A number is divisible by 10 if the last digit is 0.
Definitions
Prime Numbers: A whole number greater
than 1 that has only 1 and itself as factors.
Composite Numbers: A whole number
greater than 1 that has at least one factor
besides itself and 1.
Prime Factorization
Prime Factorization: Every composite
number can be expressed as a product of
only prime numbers.
Examples:
6
2•3
6=2•3
12
3•4
3•2•2
100
10 • 10
2•5•2•5
12 = 2 • 2 • 3 25 = 2 • 5 • 2 • 5
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
Choose all of the prime numbers
listed above by clicking on them.
You’ll hear chimes and the number will flash if
you are correct.
1
2 3
4
5
6
7
8
9 10 11 12
Choose, by clicking, all of the
composite numbers.
You’ll hear chimes and the number will flash if
you are correct.