Divisibility Rules

Page 10 in textbook

What does it mean to be divisible?

• Divisible A whole number is divisible by another number if the remainder is 0 when the first number is divided by the second.

Rule

• A whole number is divisible by 2:–if the ones digit is divisible by 2

–A whole number is EVEN if it is divisible by 2 (even #s: 0, 2, 4, 6, 8)–Examples: 2, 4, 6, 8, 10, 12, …

Are these numbers divisible by 2?

1. 2,320

2. 3,135

3. 78

4. 11,292

Rule

• A whole number is divisible by 3:–if the sum of the digits is divisible

by 3–Example: 3, 6, 9, 12, 15, 18, …

Are these numbers divisible by 3?

1) 808 + 0 = 8 Not divisible by 3!

2) 489

3) 14,980

4) 18,321

Rule

• A whole number is divisible by 4:–If the number formed by the last two

digits is divisible by 4.–Example: 4, 8, 12, …, 104, 112, …

Are these numbers divisible by 4?

1) 605look at the last 2 digits: 05 NOT divisible by 4!

2) 80

3) 9, 948

4) 11, 292

Rule

• A whole number is divisible by 5:–If the ones digit is a 0 or 5.

–Example: 5, 10, 15, 20, 25, …

Are these numbers divisible by 5?

1) 45look at the ones place: 5 YES it is divisible by 5!

2) 631

3) 385

4) 459

Rule

• A whole number is divisible by 6:–If the number is divisible by BOTH 2

and 3.–Example: 6, 12, 18, 24, 30, …

Are these numbers divisible by 6?

1) 126Check for 2: ends in 6 which is

divisible by 2Check for 3: 1 + 2 + 6 = 9 which is divisible

by 3So, YES it is divisible by 6 because it is

divisible by both 2 AND 3!2) 684

3) 2, 835

4) 1, 114

Rule

• A whole number is divisible by 9:–If the sum of the digits is divisible

by 9.–Example: 9, 18, 27, 36, 45, …

Are these numbers divisible by 9?

1) 606 + 0 = 6, So NO it is not divisible

by 92) 138

3) 900

4) 8, 505

Rule

• A whole number is divisible by 10:–If the ones digit is 0.

–Example: 10, 20, 30, 40, 50, …

Are these numbers divisible by 10?

1) 56Look at the ones place 6, so NO!

2) 220

3) 32,360

4) 654