# Factor Tree of a given Number

Factor Tree is an intuitive method to understand the factors of a number. It shows how all the factors are been derived from the number. It is a special diagram where you find the factors of a number, then the factors of those numbers, etc until you can’t factor anymore. The ends are all the prime factors of the original number.

Example:

Input : v = 48 Output : Root of below tree 48 /\ 2 24 /\ 2 12 /\ 2 6 /\ 2 3

The factor tree is created recursively. A binary tree is used.

- We start with a number and find the minimum divisor possible.
- Then, we divide the parent number by the minimum divisor.
- We store both the divisor and quotient as two children of the parent number.
- Both the children are sent into function recursively.
- If a divisor less than half the number is not found, two children are stored as NULL.

`// C++ program to construct Factor Tree for ` `// a given number ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Tree node ` `struct` `Node ` `{ ` ` ` `struct` `Node *left, *right; ` ` ` `int` `key; ` `}; ` ` ` `// Utility function to create a new tree Node ` `Node* newNode(` `int` `key) ` `{ ` ` ` `Node* temp = ` `new` `Node; ` ` ` `temp->key = key; ` ` ` `temp->left = temp->right = NULL; ` ` ` `return` `temp; ` `} ` ` ` `// Constructs factor tree for given value and stores ` `// root of tree at given reference. ` `void` `createFactorTree(` `struct` `Node **node_ref, ` `int` `v) ` `{ ` ` ` `(*node_ref) = newNode(v); ` ` ` ` ` `// the number is factorized ` ` ` `for` `(` `int` `i = 2 ; i < v/2 ; i++) ` ` ` `{ ` ` ` `if` `(v % i != 0) ` ` ` `continue` `; ` ` ` ` ` `// If we found a factor, we construct left ` ` ` `// and right subtrees and return. Since we ` ` ` `// traverse factors starting from smaller ` ` ` `// to greater, left child will always have ` ` ` `// smaller factor ` ` ` `createFactorTree(&((*node_ref)->left), i); ` ` ` `createFactorTree(&((*node_ref)->right), v/i); ` ` ` `return` `; ` ` ` `} ` `} ` ` ` `// Iterative method to find the height of Binary Tree ` `void` `printLevelOrder(Node *root) ` `{ ` ` ` `// Base Case ` ` ` `if` `(root == NULL) ` `return` `; ` ` ` ` ` `queue<Node *> q; ` ` ` `q.push(root); ` ` ` ` ` `while` `(q.empty() == ` `false` `) ` ` ` `{ ` ` ` `// Print front of queue and remove ` ` ` `// it from queue ` ` ` `Node *node = q.front(); ` ` ` `cout << node->key << ` `" "` `; ` ` ` `q.pop(); ` ` ` `if` `(node->left != NULL) ` ` ` `q.push(node->left); ` ` ` `if` `(node->right != NULL) ` ` ` `q.push(node->right); ` ` ` `} ` `} ` ` ` `// driver program ` `int` `main() ` `{ ` ` ` `int` `val = 48;` `// sample value ` ` ` `struct` `Node *root = NULL; ` ` ` `createFactorTree(&root, val); ` ` ` `cout << ` `"Level order traversal of "` ` ` `"constructed factor tree"` `; ` ` ` `printLevelOrder(root); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:

Level order traversal of constructed factor tree 48 2 24 2 12 2 6 2 3

This article is contributed by **Suprotik Dey**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Count the nodes of the given tree whose weight has X as a factor
- N-th prime factor of a given number
- k-th prime factor of a given number
- Smallest number S such that N is a factor of S factorial or S!
- Sum of largest prime factor of each number less than equal to n
- Largest factor of a given number which is a perfect square
- Find largest prime factor of a number
- Given a n-ary tree, count number of nodes which have more number of children than parents
- Prime Factor
- Least prime factor of numbers till n
- Exactly n distinct prime factor numbers from a to b
- Count all the numbers less than 10^6 whose minimum prime factor is N
- Nearest element with at-least one common prime factor
- Queries on the sum of prime factor counts in a range
- Count of subarrays whose products don't have any repeating prime factor