1. 4-1 Divisibility Warm Up Problem of the Day Lesson Presentation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Course 1
4-1
Divisibility
Warm Up
1. 20
2. 48
3. 16
Write each number as a product of two whole numbers in as many ways as possible.
1  20, 2  10, 4  5
1  48, 2  24, 3  16, 4  12, 6  8
1  16, 2  8, 4  4

3. 4-1 Divisibility Problem of the Day 6 7 10 11 16 3 2 4 15 14 1 9 12 5
Course 1
4-1
Divisibility
Problem of the Day
In this magic square, every
row, column, and diagonal
has the same sum, 34.
Complete the square
using the whole numbers
from 1 to 16.
Possible answer: 6 7 10 11 16 3 2 4 15 14 1 9 12 5 8 13

4. Course 1
4-1
Divisibility
Learn to use divisibility rules.

5. Insert Lesson Title Here
Course 1
4-1
Divisibility
Insert Lesson Title Here
Vocabulary
divisible
composite number
prime number

6. 42 ÷ 6 = 7 Quotient 4-1 Divisibility
Course 1
4-1
Divisibility
A number is divisible by another number if the quotient is a whole number with no remainder.
42 ÷ 6 = 7
Quotient

7. 4-1 Divisibility Divisibility Rules A number is divisible by. . .
Course 1
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
4 if the last two digits form a number divisible by 4.
8,512
7,518
5 if the last digit is 0 or 5.
14,975
10,978
6 if the number is divisible by both 2 and 3 48 20
9 if the sum of the digits is divisible by 9.
711 93
10 if the last digit is 0.
15,990
10,536

8. Additional Example 1A: Checking Divisibility
Course 1
4-1
Divisibility
Additional Example 1A: Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5
The last digit, 2, is even.
Divisible
The sum of the digits is = is divisible by 3.
Divisible
The last two digits form the number is not divisible by 4.
Not divisible
Not divisible
The last digit is 2.
So 462 is divisible by 2 and 3.

9. Additional Example 1B: Checking Divisibility
Course 1
4-1
Divisibility
Additional Example 1B: Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10. 6 9 10
The number is divisible by both 2 and 3.
Divisible
The sum of the digits is = is divisible by 9.
Divisible
The last digit is 0.
Divisible
So 540 is divisible by 6, 9, and 10.

10. 4-1 Divisibility Check It Out: Example 1A
Course 1
4-1
Divisibility
Check It Out: Example 1A
Tell whether 114 is divisible by 2, 3, 4, and 5. 2 3 4 5
The last digit, 4, is even.
Divisible
The sum of the digits is = is divisible by 3.
Divisible
The last two digits form the number is not divisible by 4.
Not Divisible
Not Divisible
The last digit is 4.
So 114 is divisible by 2 and 3.

11. 4-1 Divisibility Check It Out: Example 1B
Course 1
4-1
Divisibility
Check It Out: Example 1B
Tell whether 810 is divisible by 6, 9, and 10. 6 9 10
The number is divisible by both 2 and 3.
Divisible
The sum of the digits is = is divisible by 9.
Divisible
The last digit is 0.
Divisible
So 810 is divisible by 6, 9, and 10.

12. Course 1
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.

13. Course 1
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

14. Additional Example 2: Identifying Prime and Composite Numbers
Course 1
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

15. Additional Example 2: Identifying Prime and Composite Numbers
Course 1
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

16. 4-1 Divisibility Check It Out: Example 2
Course 1
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

17. 4-1 Divisibility Check It Out: Example 2
Course 1
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

18. Insert Lesson Title Here
Course 1
4-1
Divisibility
Insert Lesson Title Here
Lesson Quiz
Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, and 10.
1. 256
2. 720
3. 615
Tell whether each number is prime or composite.
divisible by 2, 4
divisible by 2, 3, 4, 5, 6, 9, 10
divisible by 3, 5
prime
composite