+0  
 
0
34
1
avatar

If $n = 2^{10} \cdot 3^{8} \cdot 5^{14}$, how many of the natural-number factors of n are multiples of 150?

 Jul 7, 2022
 #1
avatar+1105 
+8

2^10 x 3^14 x 5^8 =

 

2^1 x 3^1 x 5^2 =150

 

Subtract the exponents of the same base numbers and add 1 in each case as follows:

 

[10 - 1 + 1] x [14 - 1 + 1] x [8 - 2 + 1] =10 x 14 x 7 = 980 such numbers.

 

 

answer from guest. the link is not working for some reason.

 Jul 7, 2022

7 Online Users

avatar
avatar