1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 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. 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: 2 3 16 11 10 7 6 4 15 14 1 9 12 5 8 13

4. Learn to use divisibility rules.

5. Vocabulary
divisible
composite number
prime number

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

7. Divisibility Rules 10,536 15,990 10 if the last digit is 0. 93 711
9 if the sum of the digits is divisible by 9. 20 48
6 if the number is divisible by both 2 and 3.
10,978
14,975
5 if the last digit is 0 or 5.
7,518
8,512
4 if the last two digits form a number divisible by 4.
139
315
3 if the sum of the digits is divisible by 3.
4,975
3,978
2 if the last digit is even (0, 2, 4, 6, or 8).
Not Divisible
Divisible
A number is divisible by. . .
Divisibility Rules

8. Division by 0 is undefined.
Remember!

9. Additional Example 1A: Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5. 5 4 3 2
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.

10. Additional Example 1B: Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10. 10 9 6
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.

11. Tell whether 114 is divisible by 2, 3, 4, and 5.
Check It Out: Example 1A
Tell whether 114 is divisible by 2, 3, 4, and 5. 5 4 3 2
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.

12. Tell whether 810 is divisible by 6, 9, and 10.
Check It Out: Example 1B
Tell whether 810 is divisible by 6, 9, and 10. 10 9 6
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.

13. 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.

14. Click to see which numbers from 1 through 50 are prime.49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

15. 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

16. 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

17. 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

18. 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

19. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

20. 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.
2, 4
2, 3, 4, 5, 6, 9, 10
3, 5
prime
composite

21. Lesson Quiz for Student Response Systems
1. Tell whether 255 is divisible by 2, 3, 4, 5, 6, 9, and 10.
A. 2, 3, 4, 5, 6, 9, 10
B. 2, 3, 4, 6
C. 3, 9
D. 3, 5

22. Lesson Quiz for Student Response Systems
2. Tell whether 360 is divisible by 2, 3, 4, 5, 6, 9, and 10.
A. 2, 3, 4, 5, 6, 9, 10
B. 5, 10
C. 2, 4
D. 3, 6, 9

23. Lesson Quiz for Student Response Systems
3. Tell whether 448 is divisible by 2, 3, 4, 5, 6, 9, and 10.
A. 2, 3, 4, 5, 6, 9, 10
B. 5, 9
C. 2, 4
D. 5, 6, 9

24. Lesson Quiz for Student Response Systems
4. Find the prime number.
A. 52
B. 57
C. 59
D. 63

25. Lesson Quiz for Student Response Systems
5. Find the composite number.
A. 41
B. 61
C. 121
D. 131