Explain the rules of Divisibility ?
Divisible by 2: If the last digit is a 0, 2, 4, 6, or 8, the number is evenly divisible by 2.
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Divisible by 2
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Not Divisible by 2
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4, 12, 1006, 88, 100
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5, 13, 1007, 89, 101
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Divisible by 3: Add together the digits. If the result is evenly divisible by 3 (in other words, if the result is a multiple of 3), so is the original number.
Example 1: Is the number 2553 divisible by 3?
Step 1: Add the digits together.
(2 + 5 + 5 + 3) = 15
Step 2: Does 3 evenly divide into 15?
(15 / 3 ) = 5
The answer is yes. So 2553 is divisible by 3.
Example 2: Is the number 2554 divisible by 3?
Step 1: Add the digits together.
(2 + 5 + 5 + 4) = 16
Step 2: Does 3 evenly divide into 16?
(16/ 3) = 5 R 1
The answer is no. So 2553 is not divisible by 3.
Example 3: Is the number 4,715,448,735,448 divisibly by 3?
Step 1: Add the digits together.
(4 + 7 + 1 + 5 + 4 + 4 + 8 + 7 + 3 + 5 + 4 + 4 + 8) = 64
Now check to see if the number 64 is divisible by 3. 64 is still a pretty large number. If you do not want to go through the long-division process of dividing 64 by 3, you can keep adding the digits together until you get a number that is easier to work with.
Step 2: Add the digits together.
(6 + 4) = 10
Step 3: Does 3 evenly divide into 10?
(10 /3) = 3 R 1
The answer is no. So 64 is not divisible by 3; therefore, 4,715,448,735,448 is not divisible by 3.
Divisible by 4: Check to see if the number formed by the last two digits of the original number is divisible by 4.
Example: Is the number 291,583,791,283 divisible by 4?
Step 1: Check to see if 83 (the last two digits of the original number) is divisible by 4.
(83 / 4) = 20 R 3
The answer is no. So 291,583,791,283 is not divisible by 4.
Divisible by 5: If the last digit is a 0 or 5, the number is divisible by 5.
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Divisible by 5
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Not Divisible by 5
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5, 10, 1005, 80, 100
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4, 13, 1007, 89, 101
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Divisible by 6: If the number is divisible by both 2 and 3, then it is divisible by 6.
Example: Is the number 186 divisible by 6?
Step 1: Check to see if 186 is divisible by 2.
Since the last digit is a 6, 186 is divisible by 2.
Step 2: Check to see if 186 is divisible by 3.
(1 + 8 + 6) = 15
(15 / 3) = 5
Since 15 is divisible by 3, 186 is divisible by 3.
Therefore, since 186 is divisible by both 2 and 3, then 186 is also divisible by the number 6.
Divisible by 9: Add together all the digits; if the result is divisible by 9, then so is the original number.
Example: Is the number 78,957 divisible by 9?
Step 1: Add the digits together.
(7 + 8 + 9 + 5 + 7) = 36
Now check to see if the number 36 is divisible by 9.
Step 2: Add the digits together.
(3 + 6) = 9
Since 9 evenly divides into 9, (9 / 9 =1), 36 is divisible by 9. Therefore, 78,957 is divisible by 9.
Divisible by 10: If the number ends in a 0, then it is divisible by 10.
Example: Which number, 12345 or 123450, is divisible by 10?
The answer is 123450, because it ends in a 0. 12345 is not divisible by 10, because it ends in 5.