What is the greatest common factor of 15t and 21?

There is 1 of course.. but 1 doesn't count because were looking for the greatest number so lets try  2 ...no because 2 x ? = 15 nothing. so its not 2 . lets try 3. 
3x5=15 3x7=21. so we have 3.. lets try 4.. 4x?=15...4x?=21..nothing.lets try 5. we know 5 x 3= 15 but 5x21..nothing. so lets try 6.     6x?=15..nothing.. 6x?=21..nothing.. lets try 7..7x?=15...nothing..7x?=21..3 but we are trying to find a same number that can multiply something and get those 2 numbers. so lets try 8.. 8x?=15... nothing 8x?=21.. nothing.. lets try 9..9x?=15? nothing.
9x?=21 nothing.. lets try 10.. 10x? =15 ..nothing we cant do that.. 10x?=21 nothing.. so we have 3 so far that's the greatest common factor.. so your answer is 3