Divisibility Definitions

Divisibility measures a numbers ability to be divided by another number and produce a remainder of 0.

Divisible means a number can be divided with no remainder.

Example: 4 is divisible by 2.

Divisibility Rules

• A number is divisible by 2 if it is an even number.
  • 8 is divisible by 2.
  • 48 is divisible by 2.
  • 3,155,754 is divisible by 2.

 

• A number is divisible by 3 if the sum of each of its digits is divisible by 3.
  • 174 is divisble by 3 because 1+7+4=12 and 12/3=4
  • 36 is divisible by 3 because 3+6=9 and 9/3=3
  • 333 is divisible by 3 because 3+3+3=9 and 9/3=3

 

• A number is divisible by 4 if the last two digits are both zero or if the last two digits are divisible by 4.
  • 900 is divisble by 4 because the last two digits are both zero
  • 5548 is divisible by 4 because 48 is divisible by 4

 

• A number is divisible by 5 if the last digit is a 0 or 5.
  • 25 is divisible by 5.
  • 100 is divisible by 5.
  • 155,155 is divisible by 5.

• A number is divisible by 6 if it is even and divisible by 3.
  • 30 is divisible by 6 because it is divisible by 3 and is even.

 

• A number is divisible by 9 if the sum of all of its digits is divisible by 9.
  • 846 is divisible by 9 because 8+4+6=18 and 18/9=2
  • 900 is divisible by 9 because 9+0+0=9 and 9/9=1
  • 531 is divisible by 9 because 5+3+1=9 and 9/9=1

 

• A number is divisible by 10 if the last digit is a 0.
  • 250 is divisible by 10.
  • 100 is divisible by 10.
  • 122,220 is divisible by 10

Practice Problems:
Which of the following numbers are divisible by 2 ?
1) 105	No
2) 458	Yes
3) 870	Yes
Which of the following numbers are divisible by 3 ?
1) 285	Yes
2) 40	No
3) 120	Yes
Which of the following numbers are divisible by 4 ?
1) 300	Yes
2) 81	No
3) 1232	Yes
Which of the following numbers are divisible by 5 ?
1) 300	Yes
2) 431	No
3) 1235	Yes
Which of the following numbers are divisible by 6 ?
1) 300	Yes
2) 431	No
3) 1235	No
Which of the following numbers are divisible by 9 ?
1) 1701	Yes
2) 2376	Yes
3) 1235	No
Which of the following numbers are divisible by 10 ?
1) 300	Yes
2) 431	No
3) 1235	No