Prime number decomposition What is the fastest way to decompose the given number to prime numbers without using calculator?
Example : $$3575$$
What I do is :
$$3575 = 3 \times 10^3 + 5 \times 10^2 + 7 \times 10 + 5 = 3\times5^3\times2^3 + 5^2 \times 2^2 \times 5 + 7 \times 5 \times 2 + 5$$ 
But now I do not know how to effectively get rid of "$+$".

By inspection, the final two digits of $75$ means $3575$ is divisible by $25=5^2$. Then the result of dividing out $25$ is $\frac{3500}{25} + \frac{75}{25}=4\times 35+3 = 143=12^2-1 = 11\cdot 13$, giving $3575 = 5^2\cdot11\cdot13$ 
