How many factors does each of the following numbers have?

7^3 * 11^3 =

To find the number of factors for a given number, you need to consider the prime factorization of that number. In this case, we have the number 7^3 * 11^3.

The prime factorization of a number represents its factorization into prime numbers. In this case, we have two prime factors: 7 and 11. And each of these prime factors is raised to the power of 3.

To determine the number of factors, we need to consider all the possible combinations of these prime factors.

The general formula to calculate the number of factors of a number is to add 1 to each exponent in the prime factorization and then multiply the results together.

In our case, we have 7 raised to the power of 3, so the exponent is 3. Adding 1 to the exponent gives us 3 + 1 = 4.

Similarly, we have 11 raised to the power of 3, so the exponent is also 3. Adding 1 to the exponent gives us 3 + 1 = 4.

Now, multiply the results together: 4 * 4 = 16.

Therefore, the number 7^3 * 11^3 has 16 factors.