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Divisibility Rules

Divisibility Rules. By: Kelli Holwadel. Objective. To determine if a number is divisible by a number without doing long division, but by looking at the digits. To find factors of larger numbers. What does “divisible by” mean?. Divided evenly with no remainder. Result is a whole number.

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Divisibility Rules

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  1. DivisibilityRules By: Kelli Holwadel

  2. Objective • To determine if a number is divisible by a number without doing long division, but by looking at the digits. • To find factors of larger numbers.

  3. What does “divisible by” mean? • Divided evenly with no remainder. Result is a whole number. • The divisor must be a factor of the dividend. • Ex: 12 is “divisible by” 6 because 12/6= 2 exactly. Divisor Dividend 2 is a factor of 14

  4. What is a factor? • Divides the number so there is no remainder. • Factors are numbers that can be multiplied together. • Ex: • 2 and 3 are factors of 6 because 2x3=6. • 1 and 6 are also factors. • If a number is divisible by 6 then it is also divisible by 2 and 3.

  5. Divisibility Rules: • Can be difficult to determine if a large number is divisible by a number. • The divisibility rules is a shortcut that will make it easier for us to divide. • This pattern of rules will help us find factors of numbers. • ***All numbers are divisible by 1***

  6. Rule • A number is divisible by 2 if the last digit is even (0,2,4,6,8) • Ex: 1234567890 is divisible by 2 because 0 is even. • Ex: 21 is not divisible by 2 because 1 is odd. X

  7. Which number is NOT divisible by 2? 2054 336638 1041 Answer: 1041

  8. Rule • A number is divisible by 3 if the sum of all the digits is divisible by 3 • Ex: 153 Add the digits: 1+5+3=9 • 9/3 = 3

  9. Which number is divisible by 3? 76 369 7+6=13 3+6+9=18 13/3= 4 R1 18/3= 6 X Answer: 369

  10. Rule • A number is divisible by 4 if the last 2 digits are divisible by 4. • Or the last 2 digits are 00. • Ex: 1620 20/4=5 • Ex: 700 700/4=175

  11. Which number is divisible by 4? 9337 7916 37/4= 9 R1 16/4=4 X Answer: 7916

  12. Rule • A number is divisible by 5 if the last digit is a 0 or 5. • Ex: 543210 Divisible by 5 because last digit is 0. • Ex: 12345Divisible by 5 because last digit is 5.

  13. Which number is NOT divisible by 5? 1355 1228 840 Answer: 1228

  14. Rule • A number is divisible by 6 if it is divisible by both 2 AND 3. (factors) • The number has to be even AND sum of digits is divisible by 3 • Ex: 24 divisible by 2-even. Divisible by 3 (2+4=6) 6/3=2 • 24 is divisible by 6 • Ex: 26 divisible by 2- even. Not divisible by 3 (2+6=8) 8/3= 2 R2 • 26 is not divisible by 6X

  15. Which number is divisible by 6? 408 8800 7603 • Even • Even X odd • 8+4=12 • 12/3=4 X 8+8=16 16/3= 5R1 Answer: 408

  16. Rule • The rule for 7 is neither simple nor efficient. • The best way to see if a number is divisible by 7 is with a calculator. Ex: Use a calculator to determine if the following numbers are divisible by 7 161: Yes; 7x23 470: NO; 67R1

  17. Rule • A number is divisible by 8 if the last 3 digits are divisible by 8. • The number must be even • Ex: 15952 Number is even • 9+5+2= 16 • 16/8=2 • Divisible by 8

  18. Which number is NOT divisible by 8? 765888 57891 8+8+8= 24 8+9+1=18 24/8=3 18/8= 2R2 Answer: 57891

  19. Rule • A number is divisible by 9 if the sum of all the digits is divisible by 9. • Ex: 963 Ex: 82647 • 9+6+3=18 8+2+6+4+7=27 • 18/9=2 27/9=3

  20. Which number is divisible by 9? 376 999 289 3+7+6=16 9+9+9=27 2+8+9 16/9= 1R7 27/9=3 19/9=2R1 Answer: 999

  21. Rule • A number is divisible by 10 if the last digit is a 0. • Ex: 700,000,000

  22. Which numbers are NOT divisible by 10? 310 345 89740 555 4460 255 78630 150 100 7674210 705 23450 Answers: 555, 345, 705, 255

  23. Practice Problems Apply the rules (2-10) for 414. What numbers work?

  24. 414-Practice Problem Answers • 2: 414 Yes-even • 3: 4+1+4=9…9/3=3 Yes • X 4: 1+4= 5… 5/4=1R1 No • X 5: 414 last digit is not 0 or 5. No • 6: even (rule 2) and sum is divisible by 3. Yes • X 7: use calculator- No • X 8: 4+1+4=9…9/8= 1R1 No • 9: 4+1+4=9…9/9=1 Yes • X 10: 414 Last digit is not a zero. No

  25. Divisibility Rules help students make sense of numbers. It also helps determine factors of large numbers and helps check if a number is a multiple of another number. This will be important in math later on.

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