At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
1040k = 2*2*2*2*5*13*k to make it a square: (2*2*5*13) (2*2 *k) so k must= 5* 13 or 65
wait im not understanding this problem can you explain in details? in other words dumb it down for me
honestly i dont even know what theyre asking for
I don't really know how to explain it very well, you have to break it into its counterparts as the prime factors
why is it 65 why muktiply 13 *5
Because the 2's have counterparts but the 5 and the 13 doesn't so you can multiply them together
so we're looking for the product without duplicate numbers?
The numbers 5 and 13 can't break down any farther without becoming an irrational number
so what if there was 2x2x2x2x3x3x5x7x8?
then is it 2^2 and 3^3 and 5x7x8?
just multiply the last 3?
You divide by 2 initially as it is the smallest integer so that's why you have 2^4, at that point you can't divide be two anymore without it becoming a rational number because you are left at 65. 3 and 4 don't divide into that so the next real number that divides into it is 5 so that's why you get 5 and 13 and neither of those can be broken down anymore
can you break down the question for me cuz i dont understand the last part of the question... "such that 1040K is the square of an integer?" What does this mean?
We need to find a number k such that 1040k = 2^n for some number n. The prime factorization of 1040 is 2^4 5^1 13^1. In order for 1040k to be a square number, we need every prime factor in 1040k to be at least raised to the second power. The only numbers that are not are 5 and 13 - thus, we need one more factor of 5 and one more factor of 13. Therefore, k = 5*13 = 65.