Divisibility Rules By Kelli Holwadel t c e

Divisibility Rules By: Kelli Holwadel

t c e j Ob ive • 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. • The divisor must be a factor of the dividend. • Ex: Divi 12 is “divisible by” 6 because 12/6= 2 exactly. sor Divid end 2 is a factor of 14

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 2 x 3=6. • 1 and 6 are also

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***

Ru le • A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8) • Ex: 123456789 0 is divisible by 2 because 0 is even. • Ex: 21 is not divisible by 2 because 1 is odd. X

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

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

Which number is divisible by 763? 369 7+6=13 3+6+9=18 13/3= 4 R 1 6 Answer: 369 18/3=

Ru le • A number is divisible by 4 if the digits are divisible by 4. • Or the last 2 digits are 00. • Ex: 16 20 20/4=5 • Ex: 700/4=175 last 2

Which number is divisible by 4? 93 37 37/4= 9 R 1 16/4=4 X Answer: 79 16

Ru le • A number is divisible by 5 if the last digit is a 0 or 5. • Ex: 54321 0 Divisible by 5 because last digit is 0. • Ex: 1234 5 Divisible by 5 because last digit is 5.

Which number is NOT divisible by 5? 135 5 84 0 122 8 Answer: 1228

Ru • A number is divisible by 6 if it is divisible by le 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 both

Which number is divisible by 6? 40 8 880 0 760 ü Even ü 8+4=1 2 12/3=4 üEve n X 8+8=16 16/3= Answer: 5 R 1 3 X odd

Rul rule for 7 is neither simple nor efficient. e • • 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; 7 x 23 470: NO; 67 R 1

Rul • A number is divisible by 8 if the e are divisible by 8. • The number must be even • Ex: 15 952 Number is even 9+5+2= 16 16/8=2 Divisible by 8 last 3 digits

Which number is NOT divisible by 8? 765 888 57 891 8+8+8= 24 24/8=3 8+9+1=18 18/8= 2 R 2 Answer:

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

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

Ru le • A number is divisible by 10 if the last digit is a 0. • Ex: 700, 00 0

Which numbers are NOT 17890 310 by 10? 345 divisible 89740 555 255 4460 78630 150 7674210 705705, Answers: 555, 345, 100

Practice Problems Apply the rules (2 -10) for 414.

414 -Practice Problem Answers ü 2: 41 4 Yes-even ü 3: 4+1+4=9… 9/3=3 Yes X 4: 1+4= 5… 5/4=1 R 1 No X 5: 414 last digit is not 0 or 5. No ü 6: even (rule 2) and sum is divisible by 3. Yes X 7: use calculator- No X 8: 4+1+4=9… 9/8= 1 R 1 No ü 9: 4+1+4=9… 9/9=1 Yes X 10: 41 4 Last digit is not a zero. No

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.