4-1 Divisibility

Course 1

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm Up

1. 20

2. 48

3. 16

1 20, 2 10, 4 5

1 48, 2 24, 3 16, 4 12, 6 8

Course 1

4-1 Divisibility

Write each number as a product of two whole numbers in as many ways as possible.

1 16, 2 8, 4 4

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.

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4-1 Divisibility

6 7

10 11

16 3 2

14 1154

9 12

813

5

Possible answer:

Learn to use divisibility rules.

Course 1

4-1 Divisibility

Vocabulary

divisiblecomposite numberprime number

Insert Lesson Title Here

Course 1

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

Course 1

4-1 Divisibility

Divisibility RulesDivisibility RulesA 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

Course 1

4-1 Divisibility

Additional Example 1A: Checking Divisibility

Tell whether 462 is divisible by 2, 3, 4, and 5.

2

3

4

5Not

divisible

So 462 is divisible by 2 and 3.

The last digit, 2, is even.

The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3.

The last two digits form the number 62. 62 is not divisible by 4.

Divisible

Divisible

Not divisible

The last digit is 2.

Course 1

4-1 Divisibility

Additional Example 1B: Checking Divisibility

Tell whether 540 is divisible by 6, 9, and 10.

6

9

10

So 540 is divisible by 6, 9, and 10.

The number is divisible by both 2 and 3.

The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9.

The last digit is 0.

Divisible

Divisible

Divisible

Course 1

4-1 Divisibility

Check It Out: Example 1A

Tell whether 114 is divisible by 2, 3, 4, and 5.

2

3

4

5Not

Divisible

So 114 is divisible by 2 and 3.

The last digit, 4, is even.

The sum of the digits is 1 + 1 + 4 = 6. 6 is divisible by 3.

The last two digits form the number 14. 14 is not divisible by 4.

Divisible

Divisible

Not Divisible

The last digit is 4.

Course 1

4-1 Divisibility

Check It Out: Example 1B

Tell whether 810 is divisible by 6, 9, and 10.

6

9

10

So 810 is divisible by 6, 9, and 10.

The number is divisible by both 2 and 3.

The sum of the digits is 8 + 1 + 0 = 9. 9 is divisible by 9.

The last digit is 0.

Divisible

Divisible

Divisible

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.

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

Tell whether each number is prime or composite.

Additional Example 2: Identifying Prime and Composite Numbers

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4-1 Divisibility

A. 23divisible by 1, 23prime

B. 48divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.composite

Additional Example 2: Identifying Prime and Composite Numbers

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4-1 Divisibility

C. 31divisible by 1, 31prime

D. 18divisible by 1, 2, 3, 6, 9, 18composite

Tell whether each number is prime or composite.

Tell whether each number is prime or composite.

Check It Out: Example 2

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4-1 Divisibility

A. 27divisible by 1, 3, 9, 27composite

B. 24divisible by 1, 2, 3, 4, 6, 8, 12, 24composite

Check It Out: Example 2

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4-1 Divisibility

C. 11divisible by 1, 11prime

D. 8divisible by 1, 2, 4, 8composite

Tell whether each number is prime or composite.

Lesson QuizTell 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.

4. 47 5. 38

divisible by 2, 3, 4, 5, 6, 9, 10

divisible by 2, 4

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divisible by 3, 5

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4-1 Divisibility

prime composite