I have provided the answers at the end, however if you are interested and learning the mathematical way to solve this, I have also provided the method I find easiest.
Not divisible by 2 is just another way of saying an odd number.
To find a number that is divisible by 3, you can use a neat trick, called digital roots. What this means, is to just sum up all the digits until you have a single digit.
Example: Find the digital root of 994
9 + 9 + 4 = 22 <--- this is not a single digit, repeat the process
2 + 2 = 4, the digital root of 994 is 4
Now, when a digital root is equal to 3, 6, or 9 that means the number is divisible by 3.
So we need some number between 400 and 500, whose digital root is equal to 3, 6, or 9 and is an odd number.
This helps find the first number that meets the condition, which is:
4 + 0 + 0 = 4
4 + 0 + 1 = 5
4 + 0 + 2 = 6, but 402 is even
4 + 0 + 3 = 7
4 + 0 + 4 = 8
4 + 0 + 5 = 9 <--- 405 has a digital root of 9 and it's odd!
Now, an odd number plus an even number is an odd number. 6 is an even number and is also a multiple of 3. If we add multiples of 6 to 405, we can find the other answers.
405 + 6n, where n is an integer, will give you the other answers (just make sure you don't go over 500).
Some of the answers are:
405 + 6(0) = 405 (any answer lower than this goes below 400)
405 + 6(1) = 411
405 + 6(2) = 417
405 + 6(3) = 423
405 + 6(4) = 429
...
405 + 6(14) = 489
405 + 6(15) = 495 (any answer higher than this goes above 500)
432, 468
420, 450, 480
To get a number like this, it CANNOT be even. The number 453 is divisible by 3(goes into 453 ninenty one times), but not by 2.
450 is one of 3 possible answers.
Any number between 20 and 22.36
453
How about 450
432, 468
408 = 12 x 34
420, 450, 480
To get a number like this, it CANNOT be even. The number 453 is divisible by 3(goes into 453 ninenty one times), but not by 2.
405411417Keep adding 6.
450 is one of 3 possible answers.
The greatest number between 450 and 500 that is divisible by six is 498.
There are many numbers between 500 and 1000 divisible by 3 and 9. Any number divisible by 9 is divisible by 3. How about 900?
To find out if a number is divisible by 3 add up all it's digest and check if the total is divisible by 3. to check if a number is divisible by 2 check if the last digit is divisible by 2. So one such number is 405.
400