Write out the factorial in descending order for each number. For this example, use the factorials 10! and 4!. The factorial of 10! is expressed as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, and the factorial of 4! Is expressed as 4 x 3 x 2 x 1.
Multiply the broken out factorials of each number to get the final numeric value. For instance, 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 equals 3,628,800. Meanwhile, 4 x 3 x 2 x 1 equals 24.
Find all the factors of the smaller factorial using division. Any number that can be multiplied by another number to get the final value is a factor. For instance, since 2 x 12 equals 24, both 2 and 12 are factors of 24. To find all the factors of a factorial, write out any number that the original value can be divided by. For instance, 1 x 24 is equal to 24, 24 is equal to 2 x 12, 12 is equal to 2 x 6 and 6 is equal to 2 x 3. Therefore, the factors of 24 are 1, 2, 3, 6, 12 and 24.
Divide the value of the greater factorial by the factors of the smaller factorial, starting with the largest. For instance, divide 3,628,800 by 24. Since 3,628,800 divided by 24 equals a positive whole number -- 151,200 -- 24 is the greatest common factor or largest common prime factor. If the greater factorial is not divisible by the largest factor, then continue using the next largest factor. Do this until you find the largest factor that works.