Context: The number of positive divisors of 2^(24) − 1 is Answer question

Question

Context: The number of positive divisors of 2^(24) − 1 is Answer question

🧐 Not the exact question you are looking for?Go ask a question

Solution 1

To find the number of positive divisors of 2^(24) - 1, we can start by factoring the expression 2^(24) - 1.

Step 1: Express 2^(24) - 1 as a difference of squares. 2^(24) - 1 = (2^12)^2 - 1^2

Step 2: Apply the difference of squares formula. 2^(24) - 1 = (2^12 + 1)(2^12 - 1)

Step 3: Factorize further. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^6 - 1)

Step 4: Simplify the factors. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2^3 - 1)

Step 5: Continue simplifying. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2 + 1)(2 - 1)

Step 6: Calculate the values of the factors. 2^12 + 1 = 4097 2^6 + 1 = 65 2^3 + 1 = 9 2 + 1 = 3 2 - 1 = 1

Step 7: Multiply the values of the factors. 4097 * 65 * 9 * 3 * 1 = 2,117,763

Therefore, the number of positive divisors of 2^(24) - 1 is 2,117,763.

This problem has been solved

Solution 2

To find the number of positive divisors of 2^(24) - 1, we can start by factoring the expression 2^(24) - 1.

Step 1: Express 2^(24) - 1 as a difference of squares. 2^(24) - 1 = (2^12)^2 - 1^2

Step 2: Apply the difference of squares formula. 2^(24) - 1 = (2^12 + 1)(2^12 - 1)

Step 3: Factorize further. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^6 - 1)

Step 4: Simplify the factors. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2^3 - 1)

Step 5: Continue simplifying. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2 + 1)(2 - 1)

Step 6: Calculate the values of the factors. 2^12 + 1 = 4097 2^6 + 1 = 65 2^3 + 1 = 9 2 + 1 = 3 2 - 1 = 1

Step 7: Multiply the values of the factors. 4097 * 65 * 9 * 3 * 1 = 5662315

Therefore, the number of positive divisors of 2^(24) - 1 is 5662315.

This problem has been solved

Solution 3

To find the number of positive divisors of 2^(24) - 1, we can start by factoring the expression 2^(24) - 1.

Step 1: Express 2^(24) - 1 as a difference of squares. 2^(24) - 1 = (2^12)^2 - 1^2

Step 2: Apply the difference of squares formula. 2^(24) - 1 = (2^12 + 1)(2^12 - 1)

Step 3: Factorize further. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^6 - 1)

Step 4: Simplify the factors. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2^3 - 1)

Step 5: Continue simplifying. 2^(24) - 1 = (2^12 + 1)(2^6 + 1)(2^3 + 1)(2 + 1)(2 - 1)

Step 6: Calculate the values of the factors. 2^12 + 1 = 4097 2^6 + 1 = 65 2^3 + 1 = 9 2 + 1 = 3 2 - 1 = 1

Step 7: Multiply the values of the factors. 4097 * 65 * 9 * 3 * 1 = 5662315

Therefore, the number of positive divisors of 2^(24) - 1 is 5662315.

This problem has been solved

Similar Questions

The number of positive divisors of 224 − 1 is

Which of the following number is divisible by 24?(1 Point)26968526686476049512

How many positive divisors does the number 202410 have?

Find the number of factors of 24?Options :41068

Among all the four-digit natural numbers divisible by 24, in how many numbers does the number 24 appear?

1/2

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.