# How do you find the number of divisors of n factorial?

## How do you find the number of divisors of n factorial?

Once you have the number of factors of each prime, it’s pretty simple to count the number of divisors. If there are factors of in , then each divisor has either or factors of , So there are possibilities for each . Multiply one plus the number of factors for each and you have your answer.

## How do you find the divisors algorithm?

Finding all divisors by using “finding all prime factors” in C (faster) and up to 18 digits. The simple linear search can be improved by first throwing out all factors of 2….

1. you can change printf(“%d,”, i);printf(“%d,”, n/i); to printf(“%d,”, i); if(i !=
2. You can avoid the multiple checks for n/i !=

What are the divisors of N?

1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a trivial divisor is known as a non-trivial divisor (or strict divisor). A non-zero integer with at least one non-trivial divisor is known as a composite number, while the units −1 and 1 and prime numbers have no non-trivial divisors.

### What are the divisors of 32?

Divisors of numbers

Number Prime factorization Divisors
30 2 * 3 * 5 1, 2, 3, 5, 6, 10, 15, 30
31 31 1, 31
32 25 1, 2, 4, 8, 16, 32
33 3 * 11 1, 3, 11, 33

### How many divisors does 12 factorial have?

What is the list of divisors from 1 to 100?

Number List of Divisors
Divisors of 11 1,11
Divisors of 12 1,2,3,4,6,12
Divisors of 13 1,13
Divisors of 14 1,2,7,14

What is the easiest way to find divisors?

From the table, it’s easy to see that there are 5 x 3 = 15 divisors of 144. In general, if you have the prime factorization of the number n, then to calculate how many divisors it has, you take all the exponents in the factorization, add 1 to each, and then multiply these “exponents + 1″s together.

## What are the divisors of 8?

Divisors of numbers

Number Prime factorization Divisors
6 2 * 3 1, 2, 3, 6
7 7 1, 7
8 23 1, 2, 4, 8
9 32 1, 3, 9

## What are the divisors of 100?

What is the list of divisors from 1 to 100?

Number List of Divisors
Divisors of 97 1,97
Divisors of 98 1,2,7,14,49,98
Divisors of 99 1,3,9,11,33,99
Divisors of 100 1,2,4,5,10,20,25,50,100

What is the sum of divisors of factorial of a number?

Sum of divisors of factorial of a number. Given a number n, we need to calculate the sum of divisors of factorial of the number. Examples: Input : 4 Output : 60 Factorial of 4 is 24. Divisors of 24 are 1 2 3 4 6 8 12 24, sum of these is 60.

### How to compute factorial of a given number?

A Simple Solution is to first compute factorial of given number, then count number divisors of the factorial. This solution is not efficient and may cause overflow due to factorial computation. Below is the implementation of above approach: An efficient solution is based on Legendre’s formula. Below are the steps.

### How to find Count of divisors in N in Java?

// Legendre’s formula. // JAVA program to find count of divisors in n! // than or equal to n. // initialize all entries it as true. A value // not a prime, else true. for (int p=2; p*p<=n; p++) // Legendre’s formula.

How do you find the largest power of a factorial?

Find the largest power of k x such that n! is divisible by k x. Let’s first consider the case of prime k. The explicit expression for factorial Note that every k -th element of the product is divisible by k, i.e. adds + 1 to the answer; the number of such elements is ⌊ n k ⌋.

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