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4-1 Divisibility
I CAN use rules to determine the
divisibility of numbers.
4-1 Divisibility
Vocabulary
divisible
composite number
prime number
4-1 Divisibility
A number is divisible by another
number if the quotient is a whole
number with no remainder.
42 ÷ 6 = 7
Quotient
4-1 Divisibility
Divisibility Rules
A number is divisible by …
Divisible
2 if the last digit is even (0, 2, 4, 6, or 8). 3,978
5 if the last digit is a 0 or a 5
10 if the last digit is a 0.
Not Divisible
4,975
14,975
10,978
15,990
10,536
3 if the sum of the digits is divisible by 3.
315
139
9 if the sum of the digits is divisible by 9.
711
93
6 if the number is divisible by both 2 & 3. 48
4
if the last two digits form a number
divisible by 4.
8,512
20
7,518
4-1 Divisibility
Example 1: Checking Divisibility
A. Tell whether 462 is divisible by 2, 3, 4, 5, 6, 9, and 10.
Explanation
2
digit,
is even.
The The
last last
digit,
2, is2,even.
5
TheThe
last last
digitdigit
is not
a 5a
or5aor
0.a 0.
is not
The last digit is not a 0.
10
3
The sum of the digits is 4 + 6 + 2 = 12.
12 is divisible by 3.
9
12 is not divisible by 9.
6
462 is divisible by 2 and 3.
4
The last 2 digits, 62, are not divisible
by 4
So 462 is divisible by 2, 3, and 6.
Divisible or Not?
Divisible
Not Not
divisible
divisible
Not divisible
Divisible
Not divisible
Divisible
Not divisible
4-1 Divisibility
Example 1: Checking Divisibility
B. Tell whether 540 is divisible by 2, 3, 4, 5, 6, 9, and 10.
Explanation
Divisible or Not?
2
The last digit, 0, is even.
Divisible
5
The last digit is a 5 or a 0.
Divisible
10
The last digit is a 0.
Divisible
3
The sum of the digits is 5 + 4 + 0 = 9.
9 is divisible by 3.
Divisible
9
9 is divisible by 9.
Divisible
6
540 in divisible by 2 and 3.
Divisible
4
The last 2 digits, 40, are divisible by 4.
Divisible
So 540 is divisible by 2, 5, 10, 3, 9, 6, and 4.
4-1 Divisibility
You Try! Example 1
A. Tell whether 114 is divisible by 2, 3, 4, 5, 6, 9 and 10.
114 is divisible by 2, 3, and 6.
B. Tell whether 810 is divisible by 2, 3, 4, 5, 6, 9, and 10.
810 is divisible by 2, 5, 10, 3, 9, and 6.
4-1 Divisibility
Any number greater than 1 is divisible by at
least two numbers—1 and the number itself.
Numbers that are divisible by more than
two numbers are called composite numbers.
A prime number is divisible by only the
numbers 1 and itself. For example, 11 is a
prime number because it is divisible by only
1 and 11. The numbers 0 and 1 are neither
prime nor composite.
4-1 Divisibility
Click to see which numbers from 1 through 50
are prime.
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
4-1 Divisibility
Example 2: Identifying Prime and Composite
Numbers
Tell whether each number is prime or
composite.
A. 23
divisible by 1, 23
prime
B. 48
divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
composite
4-1 Divisibility
Example 2: Identifying Prime and Composite
Numbers
Tell whether each number is prime or
composite.
C. 31
divisible by 1, 31
prime
D. 18
divisible by 1, 2, 3, 6, 9, 18
composite
4-1 Divisibility
You Try! Example 2
Tell whether each number is prime or
composite.
C. 11
A. 27
composite
B. 24
composite
prime
D. 8
composite
4-1 Divisibility
CAN YOU use rules to determine the
divisibility of numbers?
4-1 Divisibility
Lesson Quiz
Tell whether each number is divisible by 2,
3, 4, 5, 6, 9, and 10.
1. 256 2, 4
2. 720 2, 5, 10, 3, 9, 6, 4
3. 615 5, 3
Tell whether each number is prime or
composite.
4. 47 prime
5. 38 composite
4-1 Divisibility
HOMEWORK