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  "body": "\n## Definition\n\nLet $n$ be a natural number with $n \\ge 2$.\nThe smallest prime factor of $n$ is the smallest [[prime number|0SN0MAEKYX]] $p$ such that $p \\mid n$.\nIt exists by the [[existence of a prime divisor|0SPBEDVNW1]].\n\n## Remarks\n\nThe smallest prime factor of $n$ is also the smallest divisor $d$ of $n$ with $d \u003e 1$.\nThe number $n$ is prime if and only if its smallest prime factor is $n$.\nIf $n$ is composite, its smallest prime factor $p$ satisfies $p^2 \\le n$. See [[a composite number has a prime factor at most its square root|0EB6BBMQMC]].\nFor example, the smallest prime factor of $91 = 7 \\cdot 13$ is $7$.\n\n## Explanations\n\n### L1 human\n\nDivide $n$ by $2$, then by $3$, then by $4$, and so on. The first number that divides $n$ exactly is the smallest prime factor.\nIt is always prime, because a smaller factor of it would also divide $n$ and would come earlier.\n",
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