Question 1150079
If (a)(b^4)(c^3)=1215000, where a, b and c are distinct positive integers greater than 1, what is the greatest possible value of a+b+c.
<pre>Prime factors of 1,215,000: {{{matrix(1,6, 2^3, ",", 3^5, ",", and, 5^4)}}}
FACTS: 1) "a" MUST have the largest value
       2) The order of the other 2 prime factors that come after "a" doesn't 
          MATTER, which means that we can either have: {{{matrix(1,7, b^4c^3, or, c^3b^4, "=", 3^4(2^3), or, 2^3(3^4))}}} 
This then leaves us with: {{{highlight_green(matrix(1,7, a(b^4)(c^3), "=", (5^4 * 3^1)(3^4)(2^3), "=", (625 * 3)(3^4)(2^3), "=", "1,875"(3^4)(2^3)))}}}
Thus, greatest possible value of {{{highlight_green(matrix(1,9, a + b + c, "=", "1,875", "+", 3, "+", 2, "=", "1,880"))}}}