The arithmetic mean of five natural numbers is 40 . The largest exceeds the smallest number by 10 . If is the maximum possible value for the largest of these 5 numbers, then the number of positive integral divisors of is

Step-by-step solution

Let five natural numbers be -10, x, y, z, . aligned Given, & -10+x+y+z+ 5 =40 & -10+x+y+z+ =200 & x+y+z=210-2 aligned Now, -10 42 aligned Maximum value of =48 48=2^4 3^1 Positive divisors of 48=(4+1)(1+1) =5 2=10