Greatest Common Divisor
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Question

Find the Greatest Common Divisor (GCD) of the numbers 1680 and 270.

Answer

$1680=({2}^{4})(3)(5)(7)$

$270=(2)({3}^{3})(5)$

The GCD of 1680 and 270 is the product of the least powers of each prime factor in both.

Thus the GCD of 1680 and 270

$=(2)(3)(5)$

$=30$