Can you tell whether 3247 is divisible by 2, 3, 4, …, 9 without dividing?

To do that you must know the divisibility rules of various numbers, but today we will see a few.

If a number’s last digit is divisible by 2, then the whole number is divisible by 2 (OR) we can say that any even number is divisible by 2.

14362 is divisible by 2 because 114362 has 2 at the end, 2 is divisible by 2 so 14362 is also divisible by 2.

To find weather a number is divisible by 3 OR 9, you must add all the digits of the number and find the sum. If the sum is divisible by 3 OR 9 then the number is also divisible by 3 OR 9.

To find if the number 120976 is divisible by 3 then add the digits.

1+2+0+9+7+6= 25, since 25 is not divisible by 3 then “120976” is also not divisible by 3.

To find if the number 12951 is divisible by 9 then add the digits.

1+2+9+5+1= 18 is divisible by 9, so the number is also divisible by 9.

If a number’s last 2 digits are divisible by 4 then the whole number is divisible by 4.

12340, since the last digits of 12340 is divisible by 4 then “12340” is also divisible by 4.

If the last digit of a number is 0 or 5 then the number is also divisible by 5.

457660, the last digit of 457660 is 0 so the number is also divisible by 5.

If the number is divisible by 2 and 3 then the number is also divisible by 6.

To check the number 10932 is divisible by 6, do the following steps,

a. 10932 the last digit is 2, so it is divisible by 2.

b. The sum of 1+0+9+3+2 is 15, which is divisible by 3 so the number is also divisible by 3.

c. From the above statement we found that the number 10932 is divisible by 2 & 3, so it is also divisible by 6.

If last 3 digits of the number is divisible by 8 then the number is also divisible by 8.

2986344, the last 3 digits “344” which is divisible by 8 so the number 2986344 is also divisible by 8.

If the number is divisible by 3 and 4 then the number is also divisible by 12.

To check the number 10932 is divisible by 12, do the following steps,

a. 10932 the last two digits are 32, so it is divisible by 4.

b. The sum of 1+0+9+3+2 is 15, which is divisible by 3 so the number 10932 is also divisible by 3.

c. From the above statement we found that the number 10932 is divisible by 3 & 4, so it is also divisible by 12.

Divisibility rule for number 7, 11 & 13 are little complicated. I will define them in another article. I would prefer not to follow the rules instead I will directly divide the numbers.

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