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4-1 Divisibility
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
4-1 Divisibility
Warm Up
Write each number as a product of two
whole numbers in as many ways as possible.
1. 20
1  20, 2  10, 4  5
2. 48
1  48, 2  24, 3  16, 4  12, 6  8
3. 16
1  16, 2  8, 4  4
4-1 Divisibility
Problem of the Day
In this magic square, every Possible answer:
row, column, and diagonal
4 15 14 1
has the same sum, 34.
6
7 12
9
Complete the square
5 10 11 8
using the whole numbers
from 1 to 16.
16
3
2 13
4-1 Divisibility
Sunshine State Standards
Prep for MA.6.A.5.1 Use equivalent forms of
fractions, decimals…to solve problems.
Also Review of MA.5.A.6.1
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
Not Divisible
2
if the last digit is even (0, 2, 4, 6, or 8).
3,978
4,975
3
if the sum of the digits is divisible by 3.
315
139
8,512
7,518
14,975
10,978
48
20
711
93
15,990
10,536
4 if the last two digits form a number
divisible by 4.
5
if the last digit is 0 or 5.
6
if the number is divisible by both 2 and 3.
9
if the sum of the digits is divisible by 9.
10 if the last digit is 0.
4-1 Divisibility
Remember!
Division by 0 is undefined.
4-1 Divisibility
Additional Example 1A: Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5.
2
The last digit, 2, is even.
3
The sum of the digits is 4 + 6 + 2 = 12.
Divisible
12 is divisible by 3.
4
The last two digits form the number 62.
62 is not divisible by 4.
Not
divisible
5
The last digit is 2.
Not
divisible
So 462 is divisible by 2 and 3.
Divisible
4-1 Divisibility
Additional Example 1B: Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10.
6
The number is divisible by both
2 and 3.
Divisible
9
The sum of the digits is 5 + 4 + 0 = 9.
9 is divisible by 9.
Divisible
The last digit is 0.
Divisible
10
So 540 is divisible by 6, 9, and 10.
4-1 Divisibility
Check It Out: Example 1A
Tell whether 114 is divisible by 2, 3, 4, and 5.
2
The last digit, 4, is even.
Divisible
3
The sum of the digits is 1 + 1 + 4 = 6.
6 is divisible by 3.
Divisible
4
The last two digits form the number 14.
14 is not divisible by 4.
Not
Divisible
The last digit is 4.
Not
Divisible
5
So 114 is divisible by 2 and 3.
4-1 Divisibility
Check It Out: Example 1B
Tell whether 810 is divisible by 6, 9, and 10.
6
The number is divisible by both
2 and 3.
Divisible
9
The sum of the digits is 8 + 1 + 0 = 9.
9 is divisible by 9.
Divisible
The last digit is 0.
Divisible
10
So 810 is divisible by 6, 9, and 10.
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
Additional 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
Additional 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
Check It Out: Example 2
Tell whether each number is prime or
composite.
A. 27
divisible by 1, 3, 9, 27
composite
B. 24
divisible by 1, 2, 3, 4, 6, 8, 12, 24
composite
4-1 Divisibility
Check It Out: Example 2
Tell whether each number is prime or
composite.
C. 11
divisible by 1, 11
prime
D. 8
divisible by 1, 2, 4, 8
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