Question

what's an easier way to determine all of the numbers that can go in to 250 (or any large number) rather than dividing out by trial and error on the calculator?

Answer 1

In general, this is a hard problem, but for 250, the easiest way would be to find the prime factorization, and from there find all divisors. Notice that 250 is fairly easy to factor. It ends with a 0, so it must be divisible by 10. \(250/10=25\), so we have that \[250=10\cdot25=1\cdot5\cdot5^2=2\cdot5^3\]From this you can find all divisors.

Answer 2

From this you can tell that the list of divisors is\[1,\quad 5, \quad 5^2, \quad 5^3\]\[2,\quad 2\cdot5, \quad 2\cdot5^2, \quad 2\cdot5^3\]