if p is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
"no need to actually find the product of 1 to 30 . just look at the numbers that have factors of 3 . 3 = 3 6 = 3 * 2 9 = 3 * 3 12 = 3 * 2 * 2 15 = 3 * 5 18 = 3 * 3 * 2 21 = 3 * 7 24 = 3 * 2 * 2 * 2 27 = 3 * 3 * 3 30 = 3 * 2 * 5 there are 14 3 ' s , so the largest factor of p for 3 k is 3 * 14 answer : c"
add(multiply(3, const_4), 3)