The security on many public key encryption schemes relied on the intractability of finding the integer factoring problem such as RSA scheme. However, there are great deals of researches related to the RSA factoring modulus compared with the other type of attacks RSA scheme. So the need for more methods of attacks other than RSA factoring modulus to obtain an efficient and faster algorithm to solve this problem is still essential. This paper introduces a new algorithm which attacks the RSA scheme. The suggested algorithm aims to obtain the private key of the RSA scheme and then factoring the modulus based on the public key of the RSA scheme. The new idea claimed to be more efficient than the already existed algorithms especially when the public key is small, since most of public key encryption schemes select a small encryption exponent in order to improve the efficiency of encryption. The suggested algorithm is claim to be more efficient than the already existed algorithms of attack since it is faster and takes less running time.