I'm following along in a math book I'm reading and the task at hand is to find the HCF of $270$ and $900$ using prime factorization. I know the answer is $90$ because I checked the answer at the back of the book and got it wrong.
I know that the only prime factors that go into each of them are $2, 3$ and $5.$ However I'm at a complete loss figuring out where to go from there to get $90.$
$$270 = 2\cdot 5\cdot3^3,\quad 900 = 2^2\cdot 5^2 \cdot 3^2.$$ The HCF is found by taking the smallest exponent of each distinct prime in the products. So, $$HCF(270,900) = 2\cdot 5\cdot 3^2 = 90.$$