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Divisibility Rules

Divisibility Rules. Chapter 6. 6-1 Divisibility Tests for 2, 5, 10. When you divide one number by another number and the remainder is Zero….. The first number is divisible by the second number. Divisible – can be divided without a remainder.

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Divisibility Rules

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  1. Divisibility Rules Chapter 6

  2. 6-1 Divisibility Tests for 2, 5, 10 When you divide one number by another number and the remainder is Zero….. The first number is divisible by the second number. Divisible – can be divided without a remainder

  3. You can use divisibility tests to quickly see if numbers are divisible by 2, 5, or 10

  4. Divisible by 2 A number is divisible by 2 if the last digit is an even number Even numbers: 0,2,4,6,8

  5. Divisible by 5 A number is divisible by 5 if the last digit is a 0 or 5 Examples: 340 35 10,245

  6. Divisible by 10 A number is divisible by 10 if the last digit is 0 Examples: 2,500 100 95,270

  7. Can a number be divisible by 2,5, and 10?

  8. Tell if the number 5,230 is divisible by 2, 5, or 10 Step 1 Write the number. Look at the last digit Step 2 Is the last digit even? Step 3 Is the last digit a 0 or 5? Step 4 Is the last digit a 0? 5,230 yes It is divisible by 2 yes It is divisible by 5 yes It is divisible by 10

  9. Can a number be divisible by 2,5, and 10? The number 5,230 is divisible by 2,5, and 10 YES

  10. Tell if the number 395 is divisible by 2, 5, or 10 Step 1 Write the number. Look at the last digit Step 2 Is the last digit even? Step 3 Is the last digit a 0 or 5? Step 4 Is the last digit a 0? 395 no It is not divisible by 2 yes It is divisible by 5 no It is not divisible by 10

  11. Tell if the number 628 is divisible by 2, 5, or 10 Step 1 Write the number. Look at the last digit Step 2 Is the last digit even? Step 3 Is the last digit a 0 or 5? Step 4 Is the last digit a 0? 628 yes It is divisible by 2 no It is not divisible by 5 no It is not divisible by 10

  12. YOU TRY Tell if each number is divisible by 2,5, or 10 48,296 9,990 Divisible by 2, 5, and 10 Divisible by 2 16,005 Divisible by 5

  13. 6-2 Divisibility Tests for 3,6, and 9 You can use divisibility tests to quickly see if numbers are divisible by 3, 6, or 9

  14. Let’s find our “magic number” We find our “magic number” by adding the digits of our number. We continue adding until we get a single digit “magic number”

  15. Try 471 4 + 7 + 1 = 12 1 + 2 = 3 Our “magic number” is 3

  16. Find the “magic number” 66 6 + 6 = 12 1 + 2 = 3 Magic number is 3

  17. Find the “magic number” 7,470 7 + 4 + 7 + 0 = 18 1 + 8 = 9 The “magic number” is 9

  18. Find the “magic number” 6,246 6 + 2 + 4 + 6 = 18 1 + 8 = 9 The “magic number” is 9

  19. Divisible by 3 A number is divisible by 3 if the sum of the digits is divisible by 3 Sum = answer to an addition problem

  20. Divisible by 3 A number is divisible by 3 if the “magic number” is a 3,6, or 9

  21. Divisible by 3 1,524 1 + 5 + 2 + 4 = 12 1 + 2 = 3 Magic number is 3 Is 1,524 divisible by 3? YES Is the magic number a 3,6, or 9?

  22. Divisible by 3 3,451 3 + 4 + 5 + 1 = 13 1 + 3 = 4 Magic number is 4 Is 1,524 divisible by 3? NO Is the magic number a 3,6, or 9?

  23. Divisible by 6 A number is divisible by 6 if the “magic number” is a 3,6, or 9 AND the last digit is an even number.

  24. Divisible by 6 Find the magic number 108 1 + 0 + 8 = 9 The magic number is 9 Is 108 divisible by 6? Is the magic number 3,6,or 9? Yes Is the last digit an even number? Yes YES

  25. Divisible by 6 Find the magic number 244 2 + 4 + 4 = 10 1 + 0 = 1 The magic number is 1 Is 244 divisible by 6? Is the magic number 3,6,or 9? No Is the last digit an even number? Yes NO

  26. Divisible by 6 Find the magic number 7,458 7 + 4 + 5 + 8 = 24 2 + 4 = 6 The magic number is 6 Is 7,458 divisible by 6? Is the magic number 3,6,or 9? Yes Is the last digit an even number? Yes YES

  27. Divisible by 9 A number is divisible by 9 if the magic number is 9

  28. Divisible by 9 513 5 + 1 + 3 = 9 The magic number is 9 Find the magic number YES Is 513 divisible by 9? Is the magic number 9? Yes

  29. Divisible by 9 6,246 6 + 2 + 4 + 6 = 18 1 + 8 = 9 The magic number is 9 Find the magic number YES Is 6,246 divisible by 9? Is the magic number 9? Yes

  30. Tell whether the number is divisible by 3, 6, or 9 3 and 9 3,141 9 Magic number Is it divisible by 3? Is the magic number 3,6, or 9? Yes YES Is it divisible by 6? Is the magic number 3,6, or 9? Yes NO Is it an even number? No Is it divisible by 9? Is the magic number 9? Yes YES

  31. Tell whether the number is divisible by 3, 6, or 9 3 5,109 6 Magic number Is it divisible by 3? Is the magic number 3,6, or 9? Yes YES Is it divisible by 6? Is the magic number 3,6, or 9? Yes NO Is it an even number? No Is it divisible by 9? Is the magic number 9? No NO

  32. Tell whether the number is divisible by 3, 6, or 9 3,6,and 9 6,246 9 Magic number Is it divisible by 3? Is the magic number 3,6, or 9? Yes YES Is it divisible by 6? Is the magic number 3,6, or 9? Yes YES Is it an even number? Yes Is it divisible by 9? Is the magic number 9? Yes YES

  33. YOU TRY 4,953 525,000 3 3 and 6 333 3 and 9

  34. Divisibility Test for 4 A number is divisible by 4 if the number formed by the last two digits is a multiple of four. Multiples of 4 = 4,8,12,16,20,24,32,36,40…

  35. Tell if 845,628 is divisible by 4 Step 1 Write the number 845,628 845,628 Step 2 Look at the last two digits Yes Step 3 Is this number a multiple of 4? Is 845,628 divisible by 4? YES

  36. Tell if 923,456 is divisible by 4 Step 1 Write the number 923,456 923,456 Step 2 Look at the last two digits Yes Step 3 Is this number a multiple of 4? Is 923,456 divisible by 4? YES

  37. Tell if 45,032 is divisible by 4 Step 1 Write the number 45,032 45,032 Step 2 Look at the last two digits Yes Step 3 Is this number a multiple of 4? Is 45,032 divisible by 4? YES

  38. Tell if 349,821 is divisible by 4 Step 1 Write the number 349,821 349,821 Step 2 Look at the last two digits No Step 3 Is this number a multiple of 4? Is 349,821 divisible by 4? NO

  39. YOU TRY 6,981 NO 1,980 YES 64,992,812 YES

  40. Divisibility Rules • - Last digit must be an even number • - Magic Number is 3, 6, or 9 • - Last two digits are multiple of 4 • - Last digit must be a 0 or 5 • - Divisible by 2 and 3 • - Magic Number is 9 10 - Last digit must be 0 Multiples of 4: 4,8,12,16,20,24,28,32,36,40,44,48,52, 56,60,64,68,72,76,80,84,88,92,96

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