Divisibility Tests

1
Divisibility Tests

• How can you tell quickly whether a number can be
  divided exactly by another?

2
What does DIVISIBLE mean?

• A number is DIVISIBLE by another number
• if there is no remainder after division.
• The result after division is a whole number and
  the remainder is zero.
• eg 36 divided by 12 is 3, so we say
• 36 is divisible by 12

3
DIVISIBILITY TESTS

• Divisibility by 2
• Numbers that end in 0, 2, 4, 6 or 8 can be
• divided exactly by 2.
• They are said to be divisible by 2, and are also
• called EVEN numbers.
• Numbers that are not even are called ODD.

4
DIVISIBILITY TESTS

• Divisibility by 3
• To test for divisibility by 3 (without actually
• doing the division),
• add all the digits together
• and if the sum is divisible by 3, then the
• original number is too.
• This is a divisibility test for 3.

5
DIVISIBILITY TESTS

• Divisibility by 4
• A number is divisible by 4 if its last two digits
  
• can be divided by 4.
• Can you explain why this is so?

6
DIVISIBILITY TESTS

• Divisibility by 5
• How can you tell by looking at a whole number
• if it can be divided by 5?
• State a divisibility test for 5.

7
DIVISIBILITY TESTS

• Divisibility by 6
• A number that can be divided by 6 needs to be
• able to be divided by both 2 and 3.
• Now state a divisibility test for 6.

8
DIVISIBILITY TESTS

• Divisibility by 11 and others
• Find out about other divisibility tests
• eg by 11.

9
DIVISIBILITY TESTS

• Lets test a number eg 120
• 2? Yes, because it ends in 0, so is even
• 3? Yes, because 1 2 3 6, which of course
  
• is divisible by 3!
• 4? Yes, because 20 can be divided by 4
• 5? Yes, because it ends in 5 or 0.
• 6? Yes, because it can be divided by 2 and
• by 3.

10

• Test all the numbers on this page for
• divisibility by 2, 3, 4, 5, and 6.
• Remember some may be divisible by more than
• one of these numbers and some may not be
• divisible by any of them!
• 240 27 256 81
• 711 400 111
• 91 23 108
  
• 50 343 180
• Write down your answers!