Factor Tree is an intuitive method to understand 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++ progrm 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 height of Bianry 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; }

Output:

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

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