Divisibility Rules of mathematical analysis. It is a part of concrete mathematics

1. Topic: Divisibility Rule
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2. What does divisible means?
“Divisible by” means, If you divide one number by another, the result is
a whole number without a remainder.
As an example,
24/4=6
No remainder, so 24 is divisible by 4.
13/2=6.5
The result is not a whole number, so there will be a reminder
after division. So 13 is not divisible by 2.
Every whole number is divisible by its factors,1 and itself.
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3. Divisibility by 2, 5, and 10
• Divisible by 2: A number can be divided by 2 if the last digit of that
number is even (0, 2, 4, 6, 8).
• Divisible by 5: A number is divisible by 5 if the last digit is a 5 or a 0.
• Divisible by 10: A number is divisible by 10 if the last digit is a 0.
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4. Divisibility by 3,6 and 9.
Divisible by 3: A number is divisible by 3 if the sum of the digits is 3 or
a multiple of 3.
Example: check divisibility of 5437253412 by 3
5+4+3+7+2+5+3+4+1+2=36=9 , 9 is divisible by 3 so the number
5437253412 is divisible by 3.
Divisible by 6: A number can be divided by 6 if the last digit is even and
the sum of all the digits is 3 or a multiple of 3.
Divisible by 9: A number is divisible by 9 if the sum of the digits is 9 or
a multiple of 9.
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5. Divisibility by 4 and 8.
• Divisible by 4: A number is divisible by 4 if the last two digits of that
number can be divided by 4 without reminder.
Example: Check divisibility of 76345376 by 4
Last two digits are 7 and 6 is not divisible by 4 so, the given
number is not divisible by 4.
• Divisible by 8: A number is divisible by 8 if the number made by the
last three digits will be divisible by 8 without reminder.
Example: Check divisibility of 6752573288
Last three digits are 2,8,8 and 288 is divisible by 8 so, the given
number is divisible by 8.
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