Factor Tree of a given Number


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.


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

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

  1. We start with a number and find the minimum divisor possible.
  2. Then, we divide the parent number by the minimum divisor.
  3. We store both the divisor and quotient as two children of the parent number.
  4. Both the children are sent into function recursively.
  5. 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
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)

        // 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);

// Iterative method to find height of Bianry Tree
void printLevelOrder(Node *root)
    // Base Case
    if (root == NULL)  return;

    queue<Node *> q;

    while (q.empty() == false)
        // Print front of queue and remove
        // it from queue
        Node *node = q.front();
        cout << node->key << " ";
        if (node->left != NULL)
        if (node->right != NULL)

// driver program
int main()
    int val = 48;// sample value
    struct Node *root = NULL;
    createFactorTree(&root, val);
    cout << "Level order traversal of "
            "constructed factor tree";
    return 0;


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

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