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<p>I don’t understand this question. Are you trying to show that 8 | 16 without knowing the prime factorization of 16, ie, only knowing that 2 | 16 and 4 | 16? Because you can’t. For example, 2 | 4 and 4 | 4, but 8 does not divide 4.</p>
<p>The actual thing you’re looking for only works when the divisors you’re working with are mutually prime. So if gcd(a,b)=1, then a | c and b | c => ab | c. But if gcd(a,b) is not 1, that doesn’t work.</p>
<p>By the way, math 295 does not have much number theory in it. You’ll learn a little bit about algebraic structures, and that’s fundamental to number theory. However, that’s as far as you go. What you’ll really be doing is an intro to analysis. Imagine calc I with all the theoretical underpinnings.</p>
<p>Also, math 295 is really calc I and II. There’s no 3d calc in it at all, so it’s not at all comparable to math 285.</p>