Canada Number is a number N such that the sum of the squares of the digits of N is equal to the sum of the non-trivial divisors of N, i.e. (Sum of divisors of N)- 1 – N.

125, 581, 8549, 16999…

### Check if N is an Canada number

Given a number N, the task is to check if N is an Canada Number or not. If N is an Canada Number then print “Yes” else print “No”.

Examples:

Input: N = 125
Output: Yes
Explanation:
125’s factors are 1, 5, 25, 125
and 1^2 + 2^2 + 5^2 = 30 = 5 + 25.

Input: N = 16
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to find Sum of all proper divisors of a number and subtract N and 1 from it. Also, find the sum of squares of digits of N. Now check if both the sum are the same or not. If the sum of all proper divisors and sum of squares of digits of N are equal then the number is a Canada number.

Below is the implementation of the above approach:

## C++

 `// C++ implementation for the  ` `// above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to calculate sum of ` `// all trivial divisors ` `// of given natural number ` `int` `divSum(``int` `num) ` `{ ` `    ``// Final result of summation ` `    ``// of trivial divisors ` `    ``int` `result = 0; ` ` `  `    ``// Find all divisors which ` `    ``// divides 'num' ` `    ``for` `(``int` `i = 1; i <= ``sqrt``(num); i++) { ` `         `  `        ``// if 'i' is divisor of 'num' ` `        ``if` `(num % i == 0) { ` `             `  `            ``// if both divisors are same then add ` `            ``// it only once else add both ` `            ``if` `(i == (num / i)) ` `                ``result += i; ` `            ``else` `                ``result += (i + num / i); ` `        ``} ` `    ``} ` `    ``return` `(result - 1 - num); ` `} ` ` `  `// Function to return sum ` `// of squares ` `// of digits of N ` `int` `getSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``while` `(n != 0) { ` `        ``int` `r = n % 10; ` `        ``sum = sum + r * r; ` `        ``n = n / 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to check if N is a ` `// Canada number ` `bool` `isCanada(``int` `n) ` `{ ` `    ``return` `divSum(n) == getSum(n); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Given Number ` `    ``int` `n = 125; ` ` `  `    ``// Function Call ` `    ``if` `(isCanada(n)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Java implementation for the  ` `// above approach ` `import` `java.io.*; ` `class` `GFG{ ` ` `  `// Function to calculate sum of ` `// all trivial divisors ` `// of given natural number ` `static` `int` `divSum(``int` `num) ` `{ ` `    ``// Final result of summation ` `    ``// of trivial divisors ` `    ``int` `result = ``0``; ` ` `  `    ``// Find all divisors which ` `    ``// divides 'num' ` `    ``for` `(``int` `i = ``1``; i <= Math.sqrt(num); i++) ` `    ``{ ` `         `  `        ``// if 'i' is divisor of 'num' ` `        ``if` `(num % i == ``0``) ` `        ``{ ` `             `  `            ``// if both divisors are same then add ` `            ``// it only once else add both ` `            ``if` `(i == (num / i)) ` `                ``result += i; ` `            ``else` `                ``result += (i + num / i); ` `        ``} ` `    ``} ` `    ``return` `(result - ``1` `- num); ` `} ` ` `  `// Function to return sum ` `// of squares ` `// of digits of N ` `static` `int` `getSum(``int` `n) ` `{ ` `    ``int` `sum = ``0``; ` `    ``while` `(n != ``0``) ` `    ``{ ` `        ``int` `r = n % ``10``; ` `        ``sum = sum + r * r; ` `        ``n = n / ``10``; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to check if N is a ` `// Canada number ` `static` `boolean` `isCanada(``int` `n) ` `{ ` `    ``return` `divSum(n) == getSum(n); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``// Given Number ` `    ``int` `n = ``125``; ` ` `  `    ``// Function Call ` `    ``if` `(isCanada(n)) ` `        ``System.out.println(``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `} ` ` `  `// This code is contributed by shubhamsingh10 `

## Python3

 `# Python3 implementation for the  ` `# above approach ` `import` `math ` ` `  `# Function to calculate sum of ` `# all trivial divisors ` `# of given natural number ` `def` `divSum(num): ` `     `  `    ``# Final result of summation ` `    ``# of trivial divisors ` `    ``result ``=` `0` ` `  `    ``# Find all divisors which ` `    ``# divides 'num' ` `    ``for` `i ``in` `range``(``1``, ``int``(math.sqrt(num)) ``+` `1``): ` `         `  `        ``# if 'i' is divisor of 'num' ` `        ``if` `(num ``%` `i ``=``=` `0``): ` `             `  `            ``# if both divisors are same then add ` `            ``# it only once else add both ` `            ``if` `(i ``=``=` `(num ``/``/` `i)): ` `                ``result ``+``=` `i ` `            ``else``: ` `                ``result ``+``=` `(i ``+` `num ``/``/` `i) ` `    ``return` `(result ``-` `1` `-` `num) ` ` `  `# Function to return sum ` `# of squares ` `# of digits of N ` `def` `getSum(n): ` `    ``sum` `=` `0` `    ``while` `(n !``=` `0``): ` `        ``r ``=` `n ``%` `10` `        ``sum` `=` `sum` `+` `r ``*` `r ` `        ``n ``=` `n ``/``/` `10` `    ``return` `sum` ` `  `# Function to check if N is a ` `# Canada number ` `def` `isCanada(n): ` `    ``return` `divSum(n) ``=``=` `getSum(n) ` ` `  `# Driver Code ` ` `  `# Given Number ` `n ``=` `125` ` `  `# Function Call ` `if` `(isCanada(n)): ` `    ``print``(``'Yes'``) ` `else``: ` `    ``print``(``'No'``) ` ` `  `# This code is contributed by Yatin `

## C#

 `// C# implementation for the  ` `// above approach ` `using` `System; ` `class` `GFG{ ` ` `  `// Function to calculate sum of ` `// all trivial divisors ` `// of given natural number ` `static` `int` `divSum(``int` `num) ` `{ ` `    ``// Final result of summation ` `    ``// of trivial divisors ` `    ``int` `result = 0; ` ` `  `    ``// Find all divisors which ` `    ``// divides 'num' ` `    ``for` `(``int` `i = 1; i <= Math.Sqrt(num); i++) ` `    ``{ ` `         `  `        ``// if 'i' is divisor of 'num' ` `        ``if` `(num % i == 0) ` `        ``{ ` `             `  `            ``// if both divisors are same then add ` `            ``// it only once else add both ` `            ``if` `(i == (num / i)) ` `                ``result += i; ` `            ``else` `                ``result += (i + num / i); ` `        ``} ` `    ``} ` `    ``return` `(result - 1 - num); ` `} ` ` `  `// Function to return sum ` `// of squares ` `// of digits of N ` `static` `int` `getSum(``int` `n) ` `{ ` `    ``int` `sum = 0; ` `    ``while` `(n != 0) ` `    ``{ ` `        ``int` `r = n % 10; ` `        ``sum = sum + r * r; ` `        ``n = n / 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to check if N is a ` `// Canada number ` `static` `bool` `isCanada(``int` `n) ` `{ ` `    ``return` `divSum(n) == getSum(n); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main()  ` `{ ` `    ``// Given Number ` `    ``int` `n = 125; ` ` `  `    ``// Function Call ` `    ``if` `(isCanada(n)) ` `        ``Console.Write(``"Yes"``); ` `    ``else` `        ``Console.Write(``"No"``); ` `} ` `} ` ` `  `// This code is contributed by Code_Mech `

Output:

```Yes
```

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