+117 1)Find the largest integer n for which 12^n evenly divides 20! .
2)Let A be the product of the divisors of 300. What is the sum of the distinct prime divisors of A?
3)What is the sum of all positive integers n that satisfy
lcm[n,100]=gcd(n,100)+450
+117 4)In the figure below, the largest circle has a radius of six meters. Five congruent smaller circles are placed as shown and are lined up in east-to-west and north-to-south orientations. What is the radius in meters of one of the five smaller circles?
IMAGE:
https://latex.artofproblemsolving.com/e/d/2/ed239c0851978d4e1f82ba24458bd2de9836d085.png
1 - 20! mod 12^8 = 0
2 - product(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300)=19683000000000000000000
19683000000000000000000 = 2^18 * 3^9 * 5^18
Sum = 2 + 3 + 5 = 10
3 - I could find only one value for n:
n = 250
+117 thanks, for number one if n is 0 then 12^0=1 and 1 does divde into 20! but is that realy the largest? (just asking)
