Machine translation is a process of natural language translation automation to translate text from one natural language to another natural language. Machine translation is the fastest way to process a vast amount of data and produce usable translations in any language in the world. In this paper, we deal with the design of an Amharic to Ethiopian Sign Language machine translator. Amharic is the official language of Ethiopia. Ethiopian Sign Language is a visual-gestural language used to communicate and interacting by the Ethiopian Deaf community. This study presents a factored Amharic to Ethiopian Sign Language statistical machine translation system composed of three main components. The first component is a neural network-based Amharic part of speech tagger that is used as a preprocessor to factorize the words in the parallel corpora. The second component is a factored statistical machine translator that is used to translate text from Amharic to Ethiopian Sign Language grammatical structure. The third component is a word to Ethiopian Sign Language video clip mapper which takes the translated text as an input and finds matches from the video corpus. We conducted experiments using three different machine translation approaches and compared with the evaluation result of the proposed system. The first experiment is performed using a standard phrased based statistical approach as a baseline model. The second experiment conducted using a factored phrased-based approach. The third experiment carried out by using a neural machine translation approach. Our evaluation's findings demonstrate that the use of factored phrase-based statistical translation approach effectively improves Amharic to EthSL machine translation. Our proposed factored statistical translation achieves a 35.28 BLEU score which outperforms both the baseline standard phrase-based statical machine translation model and the neural machine translation model. Keywords: Machine Translation, Statistical Machine Translation, Factored Machine Translation, Amharic to Ethiopian Sign Language Machine Translation