Determine the number of divisors of the integer 4312440.
To determine the number of divisors of an integer, we need to find all the factors of the given number and count them.
First, let's find the prime factorization of the number 4312440:
4312440 = 2^3 * 3 * 5 * 35937
Next, to find the number of divisors, we need to consider each prime factor's power and multiply them together (+1).
The prime factors are: 2, 3, 5, 35937
Counting the powers, we have:
For 2, the power is 3.
For 3, the power is 1.
For 5, the power is 1.
For 35937, the power is 1.
Now, we multiply these powers together and add 1:
(3 + 1) * (1 + 1) * (1 + 1) * (1 + 1) = 4 * 2 * 2 * 2 = 32
Therefore, the number 4312440 has 32 divisors.
Prime factors decomposition:
4312440 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 5 * 11 * 11 * 11
Divisors are 2 , 3 , 5 , 11
4 divisors.