A: 96

Find the prime factorization of the number 123,456,788.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

123,456,788 | |||||||

2 | 61,728,394 | ||||||

2 | 30,864,197 | ||||||

7 | 4,409,171 | ||||||

13 | 339,167 | ||||||

17 | 19,951 | ||||||

71 | 281 |

The prime factorization in exponential form is: 2^{2} x 7^{1} x 13^{1} x 17^{1} x 71^{1} x 281^{1}

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

123,456,788 = 2^{2} x 7^{1} x 13^{1} x 17^{1} x 71^{1} x 281^{1}

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)

d(123456788) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(123456788) = (3)(2)(2)(2)(2)(2)

d(123456788) = 96

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)(e + 1)(f + 1)

d(123456788) = (2 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1)

d(123456788) = (3)(2)(2)(2)(2)(2)

d(123456788) = 96

Take a look at the factors page to see the factors of 123,456,788 and how to find them.

Try the factor calculator.

General Questions

- How is the number 123,456,788 written in scientific notation?
- What is the absolute value of the number 123,456,788?
- What is the negative version of the number 123,456,788?
- What is the place value chart for the number 123,456,788?
- What is the digital root of the number 123,456,788?
- How many digits is in the number 123,456,788?

Factoring Questions

- What are the factors or divisors of the number 123,456,788?
- What are the prime factors of the number 123,456,788?
- What is the total number of factors of the number 123,456,788?
- What is the total number of prime factors of the number 123,456,788?
- What is the sum of all factors of the number 123,456,788 including 123,456,788?
- What is the sum of all factors of the number 123,456,788 excluding 123,456,788?
- What are the factor combinations of the number 123,456,788?
- What is the prime factorization of the number 123,456,788?

Calculation Questions

Miscellaneous Questions

- How much data will 123,456,788 bytes hold in different storage units?
- What is 123,456,788 in other base number systems?
- How is 123,456,788 spelled out in other languages or countries?
- How is 123,456,788 formatted in other languages or countries?
- How is 123,456,788 formatted as currency in different languages or countries?
- What are the different hash algorithm outputs for 123,456,788?