4-1 Divisibility Course 1 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
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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.
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Insert Lesson Title Here
divisible by 3, 5
Course 1
4-1 Divisibility
prime composite
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