What is the greatest common factor of 30a^2b^4 and 24ab^3

30. a². b⁴ and 24. a. b³

1st: 30 in prime factor = 2x3x5

2nd: 24 in prime factor = 2³ x 3

Greatest Common Factor = common factor to 1st and 2nd raised at lowest exponents:

= 2 x 3 = 6

Now same principle for a². b⁴ and a. b³: Greatest Common Factor = a. b³

At last the Greatest Common Factor of 30. a². b⁴ and 24. a. b³ = 6ab³

Prove: 30. a². b⁴ / 6ab³ = 5a. b

and 24a. b³ / 6a. b = 6b²