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Divisibility Rules

Divisibility Rules. A number is divisible by 2 . If the last digit is even Divisible : 3,97 8 Not Divisible : 4,97 5. A number is divisible by 3. If the sum of the digits is divisible by 3 Divisible: 315 (3 + 1 + 5 = 9; 9 is divisible by 3)

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Divisibility Rules

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  1. Divisibility Rules

  2. A number is divisible by 2 • If the last digit is even • Divisible: 3,978 • Not Divisible: 4,975

  3. A number is divisible by 3 • If the sum of the digits is divisible by 3 • Divisible: 315 (3 + 1 + 5 = 9; 9 is divisible by 3) • Not Divisible: 139 (1 + 3 + 9 = 13; 13 is not divisible by 3)

  4. A number is divisible by 4 • If the last two digits form a number divisible by 4. • Divisible: 8,512 (12 is divisible by 4) • Not Divisible: 7,518 (18 is not divisible by 4)

  5. A number is divisible by 5 • If the last digit is 0 or 5 • Divisible: 14,975 • Not Divisible: 10, 978

  6. A number is divisible by 6 • If the number is divisible by both 2 and 3 • Divisible: 48 • the last digit is even – divisible by 2 • 4 + 8 = 12; 12 is divisible by 3 • Not Divisible: 20 • the last digit is even – divisible by 2 • 2 + 0 = 2; 2 is not divisible by 3

  7. A number is divisible by 9 • If the sum of the digits is divisible by 9 • Divisible: 711 (7 + 1 + 1 = 9; 9 is divisible by 9 • Not Divisible: 93 (9 + 3 = 12; 12 is not divisible by 9)

  8. A number is divisible by 10 • If the last digit is 0 • Divisible: 15, 990 • Not Divisible: 10,536

  9. EXAMPLE

  10. Tell whether 741 is divisible by 2, 3, 4, 5, 6, 9, and 10 2: The last digit is odd – NO 3: 7 + 4 + 1 = 12; 12 is divisible by 3 – YES 4: The last two digits form the number 41. 41 isn’t divisible by 4 – NO 5: The last digit is 1 – NO 6: Divisible by 3, but not by 2 – NO 9: 7 + 4 + 1 = 12; 12 isn’t divisible by 9 – NO 10: The last digit is 1 – NO 741 is divisible by 3

  11. Prime Numbers Any number divisible by 1 and itself. Ex: 2, 3, 5, 7, 11, …

  12. Composite Numbers • A number greater than 1 that has 2 (or more) whole number factors EX: 6 (2, 3) 20 (2, 4, 5, 10)

  13. What number is neither prime nor composite? 1

  14. PRACTICE Tell whether each number is divisible by 2, 3, 4, 5, 6, 9, or 10

  15. 810 2: The last digit is even – YES 3: 8 + 1 + 0 = 9; 9 is divisible by 3 - YES 4: The last two digits form the number 10. 10 isn’t divisible by 4 - NO 5: The last digit is 0 - YES 6: Divisible by 2 and 3 - YES 9: 8 + 1 + 0 = 9; 9 is divisible by 9 - YES 10: The last digit is 0 – YES 810 is divisible by 2, 3, 5, 6, 9, and 10

  16. 675 2: The last digit is odd - NO 3: 6 + 7 + 5 = 18; 18 is divisible by 3 - YES 4: The last two digits form the number 75. 75 is not divisible by 4 - NO 5: The last digit is 5 - YES 6: Divisible by 3, but not by 2 - NO 9: 6 +7 + 5 = 18. 18 is divisible by 9 - YES 10: The last digit is 5 – NO 675 is divisible by 3, 5, and 9

  17. Tell whether the statement is true or false. Explain your answer. • All even numbers are divisible by 2 • TRUE

  18. Tell whether the statement is true or false. Explain your answer. • All odd numbers are divisible by 3 • FALSE • 5 is an odd number. If the last digit is 5, then the number is divisible by 5

  19. Tell whether the statement is true or false. Explain your answer. • Some even numbers are divisible by 5 • TRUE • 0 is an even number. If the last digit is 0, then it is divisible by 5.

  20. Prime or Composite????

  21. 47 Prime: (1 x 47) 57 Composite: (is divisible by 3)

  22. 95 Composite: (divisible by 5) 97 Prime: (1 x 97)

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