What is the greatest common factor of 420 and 660?

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Solution

$420 = 2 \times 2 \times 3 \times 5 \times 7$
$660 = 2 \times 2 \times 3 \times 5 \times 11$

The greatest common factor is the product of the primes in the shared factors only $2 \times 2 \times 3 \times 5 = 60$

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\frac{s i n (- 660^{0}) t a n (1050^{0}) s e c (- 420^{0})}{c o s (225^{0}) c o s e c (315^{0}) c o s (510^{0})}

\frac{s i n (- 660^{\circ}) t a n (1050^{\circ}) s e c (- 420^{\circ})}{c o s (225^{\circ}) c o s e c (315^{\circ}) c o s (510^{\circ})} =

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sin (- 420^{\circ}) cos (390^{\circ}) + cos (- 660^{\circ}) sin (330^{\circ}) = - 1

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