Primes Power Decomposition of 20!

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\[\begin{equation} \begin{aligned} 20! &= 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \\ & \times 11 \times 12 \times 13 \times 14 \times 15 \times 16 \times 17 \times 18 \times 19 \times 20 \\ &= 1 \times 2^1 \times 3^1 \times 2^2 \times 5^1 \times (2^13^1) \times 7^1 \times 2^3 \\ & \times 3^2 \times (2^15^1) \times 11^1 \times (2^23^1) \times 13 \times (2^17^1) \times (3^15^1) \\ & \times 2^4 \times 17^1 \times (2^13^2) \times 19 \times (2^25^1) \\ &= 2^{18} \times 3^8 \times 5^4 \times 7^2 \times 11 \times 13 \times 17 \times 19 \end{aligned} \end{equation}\]

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