Question

The number 26411 is completely divisible by

Answer 1

Answer:

7, you can just your calculator to test it out.

Answer 2

Answer:

Step-by-step explanation:

Where to start?

It isn't 2 and it isn't 3. You tell it's not 2 because it is an odd number.

It isn't 3 because the digits (26411 = 2 + 6 + 4 + 1 + 1) add up to 14 which is not divisible by 3, so the whole number is not divisible by 3.

It is not divisible by 5 because numbers divisible by 5 end either in 0 (which would make it even and divisible by 2) or 5. This one doesn't end in 5.

The very first number you can try is 7. That works. 3773 is the result.

The next prime to try is 11. I have a feeling that will work as well. Let's try it. It works as well. It's the symmetry of 3773 that made me look at eleven. There is a very complicated rule having to do with the odd and even places subtracted that tells you whether a number is divisible by 11 or not.

343 is the resulting number. I think that is 7^3  which is correct. So here's your answer

7 * 7 *7 * 7 * 11  is the answer. It's worthwhile to know how to do this. Factoring large numbers is one of the cornerstones of mathematics. Computers love this kind of thing.