+0  
 
0
98
3
avatar+18 

What is the largest prime multiple of the products of all even numbers through 2 to 200?

 

I'm not exactly sure what this question really means.

I'm really confused because it said 'prime multiple' and then 'products of all even numbers' 

Please help me!!!!!!

 Mar 4, 2023
 #2
avatar
0

200!! ==118305033 0245448578 0817140255 6304773068 3304239434 5395086021 9552506842 4830185524 5975013130 0382609551 6491169524 5558358737 3444882662 1766347181 5255955393 1916976653 8608640000 0000000000 0000000000

 

Note: !! is called "double factorial", which means: 200 x 198 x 196 x 194 x 192 x..........x 2

 

200!! ==2^197 × 3^48 × 5^24 × 7^16 × 11^9 × 13^7 × 17^5 × 19^5 × 23^4 × 29^3 × 31^3 × 37^2 × 41^2 × 43^2 × 47^2 × 53 × 59 × 61 × 67 × 71 × 73 × 79 × 83 × 89 × 97

 

I think by "prime multiple", they mean: prime factor with the largest exponent, which is: 2^197.

The largest "prime factor" is obviously: 97

 Mar 4, 2023
edited by Guest  Mar 4, 2023

2 Online Users

avatar
avatar