The most balanced factorization

MediumBrainteasers~9m

Write $1234567890 = a \cdot b$ with positive integers $a, b$ . Among all such factorizations, let $(a^*, b^*)$ be the one minimizing $|a - b|$ (the most balanced). Find $a^* + b^*$ .

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Balanced factors straddle $\sqrt{N}\approx 35136$ . Factor $N=2\cdot3^2\cdot5\cdot3607\cdot3803$ .
$9\cdot3803=34227$ and $2\cdot5\cdot3607=36070$ are the closest pair.

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The most balanced factorization

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