The number of positive divisors of 224 − 1 is

To find the number of positive divisors of 224 - 1, we can start by factoring the number 224 - 1.

First, let's find the prime factorization of 224. We can start by dividing it by the smallest prime number, which is 2.

224 ÷ 2 = 112

Next, we divide 112 by 2 again:

112 ÷ 2 = 56

We continue dividing by 2 until we can no longer divide evenly:

56 ÷ 2 = 28 28 ÷ 2 = 14 14 ÷ 2 = 7

Now, we have reached a prime number, 7.

So, the prime factorization of 224 is 2^5 * 7.

To find the number of positive divisors, we can use the formula (a+1)(b+1)(c+1)..., where a, b, c, etc. are the exponents of the prime factors in the prime factorization.

In this case, we have 5 as the exponent of 2 and 1 as the exponent of 7.

So, the number of positive divisors of 224 - 1 is (5+1)(1+1) = 6 * 2 = 12.