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

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

3. 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. 2 316 1110 7 6 141 15 4 912 8 13 5 Possible answer:

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

5. 4-1 Divisibility Vocabulary divisible composite number prime number

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

7. 4-1 Divisibility 10,53615,99010 if the last digit is 0. 937119 if the sum of the digits is divisible by 9. 20486 if the number is divisible by both 2 and 3. 10,97814,9755 if the last digit is 0 or 5. 7,5188,5124 if the last two digits form a number divisible by 4. 1393153 if the sum of the digits is divisible by 3. 4,9753,9782 if the last digit is even (0, 2, 4, 6, or 8). Not DivisibleDivisibleA number is divisible by... Divisibility Rules

8. 4-1 Divisibility Division by 0 is undefined. Remember!

9. 4-1 Divisibility Additional Example 1A: Checking Divisibility Tell whether 462 is divisible by 2, 3, 4, and 5. 5 4 3 2 Not 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 Not divisible The last digit is 2.

10. 4-1 Divisibility Additional Example 1B: Checking Divisibility Tell whether 540 is divisible by 6, 9, and 10. 10 9 6 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

11. 4-1 Divisibility Check It Out: Example 1A Tell whether 114 is divisible by 2, 3, 4, and 5. 5 4 3 2 Not 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 Not Divisible The last digit is 4.

12. 4-1 Divisibility Check It Out: Example 1B Tell whether 810 is divisible by 6, 9, and 10. 10 9 6 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

13. 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.

14. 4-1 Divisibility Click to see which numbers from 1 through 50 are prime. 50494847464544434241 40393837363534333231 30292827262524232221 20191817161514131211 10987654321

15. 4-1 Divisibility Tell whether each number is prime or composite. Additional Example 2: Identifying Prime and Composite Numbers A. 23 divisible by 1, 23 prime B. 48 divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. composite

16. 4-1 Divisibility Additional Example 2: Identifying Prime and Composite Numbers C. 31 divisible by 1, 31 prime D. 18 divisible by 1, 2, 3, 6, 9, 18 composite Tell whether each number is prime or composite.

17. 4-1 Divisibility Tell whether each number is prime or composite. Check It Out: Example 2 A. 27 divisible by 1, 3, 9, 27 composite B. 24 divisible by 1, 2, 3, 4, 6, 8, 12, 24 composite

18. 4-1 Divisibility Check It Out: Example 2 C. 11 divisible by 1, 11 prime D. 8 divisible by 1, 2, 4, 8 composite Tell whether each number is prime or composite.

19. 4-1 Divisibility Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 4-1 Divisibility 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. 4. 475. 38 2, 3, 4, 5, 6, 9, 10 2, 4 3, 5 prime composite

21. 4-1 Divisibility 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 Lesson Quiz for Student Response Systems

22. 4-1 Divisibility 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 Lesson Quiz for Student Response Systems

23. 4-1 Divisibility 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 Lesson Quiz for Student Response Systems

24. 4-1 Divisibility 4. Find the prime number. A. 52 B. 57 C. 59 D. 63 Lesson Quiz for Student Response Systems

25. 4-1 Divisibility 5. Find the composite number. A. 41 B. 61 C. 121 D. 131 Lesson Quiz for Student Response Systems