The rule of divisibility for 4 is if the last two numbers are divisible by 4, the whole number is as well. You can immediately disqualify odd numbers, since multiples of 4 have to be even. That qualifies 184, 92 and 5796.
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Any number that ends in an even number (0, 2, 4, 6, 8) is divisible by 2.
A number is divisible by 6 if it is divisible both by 2 and 3 1240 is even then is divisible by 2 1+2+4+0 = 7 which is not divisible by 3 then 1240 is not divisible by 3 Thus 1240 is not divisible by 6
If a number is divisible by both three and four, it's divisible by twelve.
Numbers divisible by 6 will have at least one 2 and one 3 as prime factors because 2 x 3 = 6. The same is true for 2, 4 and 8. Numbers divisible by 4 are also divisible by 2. Numbers divisible by 8 are also divisible by 4 and 2.
Using the tests for divisibility:Divisible by 3:Add the digits and if the sum is divisible by 3, so is the original number: 6 + 8 + 4 = 18 which is divisible by 3, so 684 is divisible by 3Divisible by 6:Number is divisible by 2 and 3: Divisible by 2:If the number is even (last digit divisible by 2), then the whole number is divisible by 2. 684 is even so 684 is divisible by 2.Divisible by 3:Already shown above to be divisible by 3. 684 is divisible by both 2 & 3 so 684 is divisible by 6Divisible by 9:Add the digits and if the sum is divisible by 9, so is the original number: 6 + 8 + 4 = 18 which is divisible by 9, so 684 is divisible by 9Thus 684 is divisible by all 3, 6 & 9.