Factoring of Numerical Problems

Many problems that appear computationally intensive can be simplified by factoring out a common number. This technique reduces complex calculations into simpler steps, often combining factoring with other tricks like the 11's trick or knowledge of squares.

For example, instead of calculating two separate two-digit multiplications in $48 \times 11 + 44 \times 12$, you can factor out 11:

$48 \times 11 + (4 \times 11) \times 12 = 11 \times (48 + 4 \times 12) = 11 \times (48 + 48) = 11 \times 96 = 1056$.

Look for opportunities to factor whenever a problem seems to require a lot of dense computation at first glance.