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Q: When a 3-digit number has the same digits it is divisible by 11?

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(The assumes that "the number" in the question is not n, although if they are they same number, this is still true.) "If the sum of the digits of the number is divisible by n, then the number itself is divisible by n" is true if n is 3 or if n is 9.

add all the digits of the number and check if it is divisible by 3. eg-3321=3+3+2+1=9=divisible by three.the same works for 9.

Check the sum of the digits, if the sum divisible by 3 then the number is divisible by 3. Example 910: the sum of digits= 9 + 1 + 0 = 10, but 10 is not divisible by 3, so the number 910 is not divisible by 3. Example 2154: the sum of digits = 2 + 1 + 5 + 4 = 12, this sum is divisible by 3, so the number 2154 is divisible by 3. if the sum is long you can check the sum of the sum and apply the same rule. Example 52498731: the sum of digits = 5 + 2 + 4 + 9 + 8 + 7 + 3 + 1 = 39, the sum of the digits for 39 = 3 + 9 = 12, so the original number, i.e. 52498731 is divisible by 3.

2 is the only even prime any number ending in 2 is divisible by 2 and not prime any even number greater than 2 is divisible by 2 and not prime unless i misunderstood there can be no answer

add all digits in a number together over and over until you can't anymore and if that's divisible by three the whole number is divisible by three. eg: is 324 divisible by three? let's find out. 3+2+4=? 3 2 +4 ___ 9 and since 9 is divisible by three so is 324. same rule applies with 9.

There are 3 identical digits in the units period. If the number started with 23 then 2 + 3 = 5 and 20 - 5 = 15 which is divisible by three. If the number started with 24 then 2 + 4 = 6 and 20 - 6 = 14 is not divisible by 3. So the number is 23,000,555.

An eight digit number with one zero cannot remain the same when its digits are reversed. It must have an even number of 0s.

Yes. If a number is divisible by another number, that second number is a factor of the first. 6 is divisible by 2, 2 is a factor of 6.

five digits number when you multiply by four is the same the number when you reversed it is 21978*4 = 87912

No. (Assuming a three digit number is in the range 100-999 and excludes leading zeros, that is 080 does not count as it is really 80 which is a two digit number) To be divisible by 11, the difference in the sums of the alternate digits of the number must be divisible by 11 (or 0). For a three digit number, this means that the sum of the first and last digits less the second digit must be a multiple of 11 (or 0). For a three digit number with all the digits the same, this calculation results in the value of one of the digits (eg 333 → 3 + 3 - 3 = 3) which will not be 0, and cannot be a multiple of 11 as a single digit is less than or equal to 9 which is less than 11 and thus not a multiple of 11.

If a number is divisible by 4, it also means that the same number is divisible by 2. But if the number ends in a 3, it can't be divisible by 2 and, to a further extent, can't be divisible by 4.

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