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  "body": "\n## Definition\n\nLet $n$ be a positive integer.\nA prime factorization of $n$ is a finite list of [[prime numbers|0SN0MAEKYX]] $p_1 \\le p_2 \\le \\dots \\le p_k$ such that $n = p_1 p_2 \\cdots p_k$.\nFor $n = 1$, the prime factorization is the empty list, with the empty product $1$.\n\n## Remarks\n\nWe often group equal primes and write $n = q_1^{e_1} q_2^{e_2} \\cdots q_r^{e_r}$, with distinct primes $q_1 \u003c \\dots \u003c q_r$ and exponents $e_i \\ge 1$.\nFor example, the prime factorization of $360$ is $2, 2, 2, 3, 3, 5$, that is, $360 = 2^3 \\cdot 3^2 \\cdot 5$.\nEach positive integer has [[a prime factorization|020K0X7HVR]], and the [[fundamental theorem of arithmetic|084HH1NDCB]] says that it is unique.\n\n## Explanations\n\n### L1 human\n\nA prime factorization breaks a number into primes, which you cannot break further.\nA factor tree does this: $360 = 36 \\cdot 10 = (6 \\cdot 6) \\cdot (2 \\cdot 5) = 2 \\cdot 3 \\cdot 2 \\cdot 3 \\cdot 2 \\cdot 5$.\nSort the primes to get the list $2, 2, 2, 3, 3, 5$.\n",
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