elementary number theory - Is there a better way to factor $375007$ with out testing first $612$ primes? No calculators please

Is there a better way to factor $375007$ with out testing first $612$ primes ?

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I know this factors to $31\times 12097$ by testing the primes $2,3,5,\ldots,31$.
Is there any other clever way to work this ? I have tried Fermat's factorization by writing the number as $x^2-y^2$ but it is also taking too many iterations because the factors differ by large magnitude.

Also I have been trying to factor it by changing the base to 10^2 : $37x^2 + 50x+7 = (ax+b)(cx+d)$ and other bases but no success yet.