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is divisible

To find out if a number is divisible by another number without rest there are some easy rules for some special cases:

Is this number ...

divisible by 1?

All numbers are divisible by 1.

divisible by 10?

A number is divisible by 10 if it ends with a 0.

divisible by 5?

A number is divisible by 5 if it ends either with a 0 or with a 5.

divisible by 2?

A number is divisible by 2 if it is an even number, that is all numbers that end in 0,2,4,6 or 8.
(yes, 0 is an even number)

divisible by 3?

A number is divisible by 3 if the sum of the digits are divisible by 3.
Or you take the sum of the digits repeatedly until it is smaller than 10 and then the sum must be either 3,6 or 9.
example: 93: sum of the digits 9 + 3 = 12, again sum of the digits 1 + 2 = 3 or you know from your division table that 12:3=4
(to show you that it is right: you know that 93 = 90+3; 90 is 3 * 30 and 30 : 3 = 10. And you know that 3:3 = 1) another example: 51: sum of the digits: 5 + 1 = 6 (to show you that it is right: you know that 51 = 30 + 21, 30:3 = 10, 21 : 3 = 7)

divisible by 9?

A number is divisible by 9 if the sum of the digits are divisible by 9.
That is the sum of the digits must be 9. If the sum is bigger than 9 you take the sum of the digits again until you get a number smaller than 10. If it is 9 it is divisible by 9.
example: 126: sum of the digits 1 + 2 +6 = 9
(to show you that it is right: you know that 126 = 90 + 36, 90:9=10; 36:9=4)

divisible by 6?

A number is divisible by 6 if it is divisible by 2 and divisible by 3 (that means divisible by both 2 and 3) which you can check by the rules stated above. (6 = 3 * 2)

divisible by 4?

A number is divisible by 4 if the last 2 digits of the number are divisible by 4.
This rule is not as easy as the ones above as you need to know if a number up to 99 is divisible by 4 before the rule is of any use.
100 is divisible by 4. You can write 100 = 40 + 40 + 20. 40:4 = 10 and 20:4=5. That way you know that all multiples of 100 are also divisible by 4. That is 200, 300 etc. are all divisible by 4.
To see if a number like 76 is divisible by 4 you need to calculate. Take the number and subtract 40. You know that 40 is divisible by 4. So 76 - 40 = 36. And from your division table you know that 36:4 = 9.
Another example: 96. You know that 100 is divisible by 4 and 96 + 4 = 100 so 96 is divsible by 4.
Another example: 84. subtract 40: 84-40 = 44. Again subtract 40. 44-40=4. And 4 is divisible by 4 so 84 is divisible by 4.
Another example: 532: you only need to look at the last two digits which is 32. And 32:4=8, so 532 is divisible by 4.

divisible by 8?

A number is divisible by 8 if the last 3 digits are divisible by 8.
1000 is divisible by 8. (It's 125.)

divisible by 11?

A number is divisible by 11 when the difference between the sum of the digits of even rank and the sum of the digits of odd rank is either a multiple of 11 or 0.
This sounds a bit complicated but is really very easy. It's best seen by an example: 502 458 (5 + 2 +5 = 12 and 8+4+0 = 12; 12-12 =0)
868 615 (1+8+8=17 and 5 + 6 + 6 = 17; 17-17=0)
8 686 194 (9+6+6=21 and 4+1+8+8 =21 21-21=0)
9614 ( 1 + 9 = 10 and 4 + 6 = 10, the difference 10-10 =0)
919 380 (9+9+8 = 26 ; 1+3+0 = 4; 26 - 4 = 22 = 2*11)

divisible by 12?

A number is divisible by 12 if it is divisible by 3 and 4, that means if it is divisible by both 3 and 4 which you can check with the rules above.

divisible by 15?

A number is divisible by 15 if it is divisible by 3 and 5, that means if it is divisible by both 3 and 5 which you can check with the rules above.

divisible by 16?

A number is divisible by 16 if the last 4 digits are divisible by 4. (a bit difficult, I know).

divisible by 24?

A number is divisible by 24 if it is divisible by 3 and 8, that means if it is divisible by both 3 and 8 which you can check with the rules above.

divisible by 100?

A number is divisible by 100 if the last 2 digits are 00.

divisible by 1000?

A number is divisible by 1000 if the last 3 digits are 000.

divisible by 25?

A number is divisible by 25 if the last 2 digits are either 00 or a multiple of 25, that is if the last 2 digits are either 25, 50, 75 or 00.

divisible by 125?

1000 is divisible by 125 (1000:125=8). Therefore: A number is divisible by 125 if the last 3 digits are 000 or a multiple of 125, that is if the last 3 digits are either 125, 250, 375, 500, 625, 750, 875 or 000.

divisible by 20?

A number is divisible by 20 if the last 2 digits are either 00, 20, 40, 60 or 80.

divisible by 40?

A number is divisible by 40 if it is divisible by 5 and 8, that means if it is divisible by both 5 and 8 which you can check with the rules above.

divisible by 80?

A number is divisible by 80 if it is divisible by 5 and 16, that means if it is divisible by both 5 and 16 which you can check with the rules above. But yes, I know that to find out if a number is divisible by 16 was already quite hard... Still nice to know. ;)