Any three consecutive integers are divisible by three because it can be shown that the sum divided by three is the middle number.
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If you had tried the first such set you would have seen that the answer is no. 1+2+3+4 = 10 which is not divisible by 4.
No. 26 for instance the sum of the digits is 8 but not divisible by 4. 32 the sum of the digits is 5 but divisible by 4 The rules for some other numbers are 2 all even numbers are divisible by 2 3 The sum of the digits is divisible by 3 4 The last 2 numbers are divisible by 4 5 The number ends in a 0 or 5 6 The sum of the digits is divisible by 3 and is even 7 no easy method 8 The last 3 numbers are divisible by 8 9 The sum of the digits is divisible by 9
The sum of three consecutive odd numbers must be divisible by 3. As 59 is not wholly divisible by 3 the question is invalid. PROOF : Let the numbers be n - 2, n and n + 2. Then the sum is 3n which is divisible by 3. If the question refers to three consecutive numbers then a similar proof shows that the sum of these three numbers is also divisible by 3. Again, the question would be invalid.
There are eight pairs of numbers divisible by three that sum to 150, and 75 is also divisible by three, so: sum = 17 * 75 = 750 + 525 = 1275
A number is divisible by 3 if the sum of its digits is divisible by 3.