Factorial and Multiple

AtCoder

IDabc280_d

Time2000ms

Memory256MB

Difficulty—

You are given an integer $K$ greater than or equal to $2$. Find the minimum positive integer $N$ such that $N!$ is a multiple of $K$. Here, $N!$ denotes the factorial of $N$. Under the Constraints of this problem, we can prove that such an $N$ always exists. ## Constraints * $2\leq K\leq 10^{12}$ * $K$ is an integer. ## Input The input is given from Standard Input in the following format: $K$ [samples]

Samples

Input #1

Output #1

5

*   $1!=1$
*   $2!=2\times 1=2$
*   $3!=3\times 2\times 1=6$
*   $4!=4\times 3\times 2\times 1=24$
*   $5!=5\times 4\times 3\times 2\times 1=120$

Therefore, $5$ is the minimum positive integer $N$ such that $N!$ is a multiple of $30$. Thus, $5$ should be printed.

Input #2

123456789011

Output #2

123456789011

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Factorial and Multiple",
    "description": {
      "content": "You are given an integer $K$ greater than or equal to $2$.   Find the minimum positive integer $N$ such that $N!$ is a multiple of $K$. Here, $N!$ denotes the factorial of $N$. Under the Constraints o",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc280_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $K$ greater than or equal to $2$.  \nFind the minimum positive integer $N$ such that $N!$ is a multiple of $K$.\nHere, $N!$ denotes the factorial of $N$. Under the Constraints o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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