#AT1063. C - Digits in Multiplication
C - Digits in Multiplication
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C - Digits in Multiplication
Score : $300$ points
Problem Statement
You are given an integer $N$.
For two positive integers $A$ and $B$, we will define $F(A,B)$ as the larger of the following: the number of digits in the decimal notation of $A$, and the number of digits in the decimal notation of $B$.
For example, $F(3,11) = 2$ since $3$ has one digit and $11$ has two digits.
Find the minimum value of $F(A,B)$ as $(A,B)$ ranges over all pairs of positive integers such that $N = A \times B$.
Constraints
- $1 \leq N \leq 10^{10}$
- $N$ is an integer.
Input
The input is given from Standard Input in the following format:
Output
Print the minimum value of $F(A,B)$ as $(A,B)$ ranges over all pairs of positive integers such that $N = A \times B$.
10000
3
$F(A,B)$ has a minimum value of $3$ at $(A,B)=(100,100)$.
1000003
7
There are two pairs $(A,B)$ that satisfy the condition: $(1,1000003)$ and $(1000003,1)$. For these pairs, $F(1,1000003)=F(1000003,1)=7$.
9876543210
6