Divisibility Rules

Skip Counting

1) Skip count by 3 from 3.

2) Skip count by 5 from 65.

3) Skip count by 10 from 1230.

4) Skip count by 6 from 138.

Double and Halve

1) 8 x 45

2) 4 x 150

3) 1.5 x 12

Repeated Doubling

1) Double 2. Double the next number. Repeat.

2) Double 3. Double the next number. Repeat.

1) Find a number with 5 factors.

2) Draw a factor tree for each of the following:a) 10 b) 17 c) 27

Divisibility

A number is divisible by another number if the answer is a whole number.

dividend ÷ divisor = quotient

A number is divisible if the quotient is a whole number.

Which of the following are divisible by 2? By 5? By 10?

• 78

• 27

• 35

• 410

• 123

• 2100

• 4126

• 795

   

 A number is divisible by:

2 if the number is even (ends in 0, 2, 4, 6, or 8)

3  

4

5 if the ones digit is 0 or 5  

6

8

9

10 if the ones digit is 0 

Multiples of 3

Write the first 10 multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Notice anything?

1) Shade all of the multiples of 3 in yellow.

2) Choose a two-digit multiple of 3. Add the digits. Is the result divisible by 3?

3) Repeat with another two-digit multiple of three.

4) Write a divisibility rule for 3.

1) Shade all of the multiples of 2 in blue.

2) Which numbers are multiples of both 2 and 3?

3) Can you describe the pattern of the green squares?

4) What other number (not 1) can these numbers be divided by?

5) Write a divisibility rule for 6.

Multiples of 9

Write the first 10 multiples of 9.

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Notice anything?

783

5886

6579

99 999

   

 A number is divisible by:

2 if the number is even (ends in 0, 2, 4, 6, or 8) 

3 if the sum of the digits is divisible by 3 

4

5 if the ones digit is 0 or 5  

6 if it is divisible by 2 and 3  

8

9 if the sum of the digits is divisible by 9  

10 if the ones digit is 0 

Which of the following numbers are divisible by 3?

630 1701 960 1412

324 6313 5241 28 312

885 7038 136 5382

Which of the following numbers are divisible by 6?

876 789 888 8433

9243 84 856 4914

25 623 7254 2254 6273

Which of the following numbers are divisible by 9?

270 216 300 4572

2613 108 8361 70 245

2015 5409 5230 47 390

Use a 300-399 hundreds chart

1) Circle all the numbers that are divisible by 2.

2) Use a different colour. Circle all the numbers that are divisible by 4.

3) What do you notice?

4) Use a different colour. Circle all the numbers that are divisible by 8.

5) What patterns do you see?

If a number is divisible by 8, what else can we say about it?

If a number is divisible by 4, what else can we say about it?

A number is divisible by 4 if the number formed by the digits in the tens and ones place is divisible by 4.

We can also say that numbers that can be divided by 4 can be divided by 2 twice.

Examples: 44, 72, 88

A number is divisible by 8 if the number formed by the digits in the hundreds, tens, and ones place is divisible by 8.

In other words, a number is divisible by 8 if it is divisible by 2 three times.

Examples: 520, 272, 7896

   

 A number is divisible by:

2 if the number is even (ends in 0, 2, 4, 6, or 8) 

3 if the sum of the digits is divisible by 3 

4 if the last two digits are divisible by 4

5 if the ones digit is 0 or 5  

6 if it is divisible by 2 and 3  

8 if the last three digits are divisible by 8

9 if the sum of the digits is divisible by 9  

10 if the ones digit is 0 

Which of the following numbers are divisible by 4?

324 630 7168 3354

84 248 742 6082

35 636 480 2616 1 003 004

Which of the following numbers are divisible by 8?

324 630 7168 3464

654 248 742 6280

35 636 480 2616 1 003 056