1. 4-1 Divisibility I CAN use rules to determine the divisibility of numbers.

2. 4-1 Divisibility Vocabulary divisible composite number prime number

3. 4-1 Divisibility A number is divisible by another number if the quotient is a whole number with no remainder. 42 ÷ 6 =7Quotient

4. 4-1 Divisibility Divisibility Rules A number is divisible by …DivisibleNot Divisible if the last digit is even (0, 2, 4, 6, or 8).2 5 10 3 9 6 4 if the last digit is a 0 or a 5 if the last digit is a 0. if the sum of the digits is divisible by 3. if the sum of the digits is divisible by 9. if the number is divisible by both 2 & 3. if the last two digits form a number divisible by 4. 3,978 4,975 14,975 10,978 15,990 10,536 315139 71193 4820 8,5127,518

5. 4-1 Divisibility Example 1: Checking Divisibilit y A. Tell whether 462 is divisible by 2, 3, 4, 5, 6, 9, and 10. So 462 is divisible by 2, 3, and 6. The last digit, 2, is even. Not divisible The last digit is not a 5 or a 0. ExplanationDivisible or Not? 2 5 10 3 9 6 4 Divisible The last digit, 2, is even. The last digit is not a 5 or a 0. Not divisible The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3. Divisible The last digit is not a 0. Not divisible Divisible 12 is not divisible by 9. 462 is divisible by 2 and 3. The last 2 digits, 62, are not divisible by 4

6. 4-1 Divisibility Example 1: Checking Divisibility B. Tell whether 540 is divisible by 2, 3, 4, 5, 6, 9, and 10. So 540 is divisible by 2, 5, 10, 3, 9, 6, and 4. ExplanationDivisible or Not? 2 5 10 3 9 6 4 Divisible The last digit, 0, is even. The last digit is a 5 or a 0. Divisible The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 3. Divisible The last digit is a 0. Divisible 9 is divisible by 9. 540 in divisible by 2 and 3. The last 2 digits, 40, are divisible by 4.

7. 4-1 Divisibility You Try! Example 1 A. Tell whether 114 is divisible by 2, 3, 4, 5, 6, 9 and 10. 114 is divisible by 2, 3, and 6. B. Tell whether 810 is divisible by 2, 3, 4, 5, 6, 9, and 10. 810 is divisible by 2, 5, 10, 3, 9, and 6.

8. 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.

9. 4-1 Divisibility Click to see which numbers from 1 through 50 are prime. 50494847464544434241 40393837363534333231 30292827262524232221 20191817161514131211 10987654321

10. 4-1 Divisibility Tell whether each number is prime or composite. 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

11. 4-1 Divisibility 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.

12. 4-1 Divisibility Tell whether each number is prime or composite. You Try! Example 2 A. 27 composite B. 24 composite C. 11 prime D. 8 composite

13. 4-1 Divisibility CAN YOU use rules to determine the divisibility of numbers?

14. 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, 5, 10, 3, 9, 6, 4 2, 4 5, 3 prime composite

15. 4-1 Divisibility HOMEWORK