The chronology of Joseph’s life is not as easy as the chronology of the rest of Genesis. While Genesis does tell us how old Joseph was when certain events happened, Genesis does not tell us how old Jacob was when he had Joseph, and therefore we cannot work out the dates of the events of the life of Joseph based upon the date of his birth as we did for everyone else. Instead we need to compare certain events in Jacob’s life against the same events in Joseph’s life.
We know that Jacob was 130 years old when he arrived in Egypt (Genesis 47:9), which means that Jacob arrived in Egypt in the year 2298 AM. We know that Jacob arrived in Egypt in the Second year of a 7 year famine (Genesis 45:6) which places the start of the famine in 2296 AM and that the famine had 5 years remaining after Jacob arrived in Egypt (Genesis 45:11) which places the end of the seven year famine in 2303 AM. The seven years of famine was preceded by seven good years (Genesis 41:26,27) which means that the seven good years started in 2289 AM. At the start of the seven good years, Joseph interprets Pharoah’s dream, and we know from Genesis 41:26,27 that Joseph was 30 when he appeared before Pharoah. Therefore Joseph was 30 years old in the year 2289 AM. We now have what we need to work everything else out.
Joseph was in prison for two years between interpreting the dreams of the Butler and Baker, and interpreting the dreams of Pharoah (Genesis 41:1), which means he interpreted the dreams of the Butler and Baker in the year 2287 AM. Joseph was seventeen when he received the coat of many colours, had his dreams, and ended up in Egypt (Genesis 37:2), which was 13 years prior to interpreting the dream of Pharoah in 2289 AM, which takes us back to 2276 AM. Being seventeen at this point means that Joseph was born 17 years earlier, meaning that he was born in 2259 AM. He then died at 110 (Genesis 50:26) which means he died in the year 2369 AM.