In this article, we propose a (2, 3)-threshold secret sharing scheme for a secret \(N\in \mathbb {N}\) ( \({>}1\) ). The secret N is encoded with the help of the Fundamental Theorem of Arithmetic (FTA), which gives (i) a set of prime factors known as the prime set and (ii) a multiplicity of the prime factors called an exponent list. A strictly binary tree is defined using the prime set, and the traversal sequences preorder,  inorder, and postorder are considered part of the shares. Here, any two traversal sequences are sufficient to reconstruct the tree. From the exponent list, three sub-lists are defined so that the merging of any two sub-lists gives the original exponent list. An individual sub-list is also included in the shares. To define the shares of the secret N, a traversal sequence is merged with a sub-list. We must return the strictly binary tree and the exponent list to reconstruct the secret N. Most of the time, the average length of the shares, given the proposed method, is almost the same as the length of the secret. Also, the secret reconstruction method is straightforward.