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

Course 1 4-1 Divisibility 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

4-1 Divisibility Problem of the Day 6 7 10 11 16 3 2 4 15 14 1 9 12 5 Course 1 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. Possible answer: 6 7 10 11 16 3 2 4 15 14 1 9 12 5 8 13

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

Insert Lesson Title Here Course 1 4-1 Divisibility Insert Lesson Title Here Vocabulary divisible composite number prime number

42 ÷ 6 = 7 Quotient 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

4-1 Divisibility Divisibility Rules A number is divisible by. . . Course 1 4-1 Divisibility Divisibility Rules A 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

Additional Example 1A: Checking Divisibility Course 1 4-1 Divisibility Additional Example 1A: Checking Divisibility Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5 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 Course 1 4-1 Divisibility Additional Example 1B: Checking Divisibility Tell whether 540 is divisible by 6, 9, and 10. 6 9 10 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.

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

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

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

Additional Example 2: Identifying Prime and Composite Numbers Course 1 4-1 Divisibility 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 Course 1 4-1 Divisibility 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

4-1 Divisibility Check It Out: Example 2 Course 1 4-1 Divisibility 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

4-1 Divisibility Check It Out: Example 2 Course 1 4-1 Divisibility 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

Insert Lesson Title Here Course 1 4-1 Divisibility Insert Lesson Title Here 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 divisible by 2, 4 divisible by 2, 3, 4, 5, 6, 9, 10 divisible by 3, 5 prime composite