Let n be an odd integer with exactly 11 positive divisors. Find the number of positive divisors of 8n^3

124

Step-by-step explanation:

As we know, the total number of positive divisors of n is the product of one more than each exponent in the prime factorization of n.

We know this product is equal to 11.

Since 11 is prime, so there can be only one number in this product, so the prime factorization of n must be , where p is a prime number.

We take a cube of the prime factorization of n to give us a prime factorization for

We see that positive divisors.

Now,

Totald divisiors =

Hence, the number of positive divisors of

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.