Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to use divisibility rules.

Vocabulary divisible composite number prime number

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

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

Division by 0 is undefined. Remember!

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 4 + 6 + 2 = 12. 12 is divisible by 3. Divisible The last two digits form the number 62. 62 is not divisible by 4. Not divisible Not divisible The last digit is 2. So 462 is divisible by 2 and 3.

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 5 + 4 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 540 is divisible by 6, 9, and 10.

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 1 + 1 + 4 = 6. 6 is divisible by 3. Divisible The last two digits form the number 14. 14 is not divisible by 4. Not Divisible Not Divisible The last digit is 4. So 114 is divisible by 2 and 3.

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 8 + 1 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 810 is divisible by 6, 9, and 10.

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.

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

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

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

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

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

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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. 47 5. 38 2, 4 2, 3, 4, 5, 6, 9, 10 3, 5 prime composite

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

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

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

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

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