How do you find the sum of the divisors of a number?

How do you find the sum of the divisors of a number?

In general, if you have the prime factorization of the number n, then to calculate the sum of its divisors, you take each different prime factor and add together all its powers up to the one that appears in the prime factorization, and then multiply all these sums together!

How do you easily find whether a number is prime or not?

To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can’t be a prime number. If you don’t get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).

What is the fastest way to find prime divisors?

The steps for calculating the prime factors of a number is similar to the process of finding the factors of any number.

1. Start dividing the number by the smallest prime number i.e., 2, followed by 3, 5, and so on to find the smallest prime factor of the number.
2. Again, divide the quotient by the smallest prime number.

How many divisors of a number are prime?

A prime number is a positive integer that has exactly two distinct whole number factors (or divisors), namely 1 and the number itself.

What is the number of divisors of 864?

864 (eight hundred sixty-four) is an even three-digits composite number following 863 and preceding 865. In scientific notation, it is written as 8.64 × 102. The sum of its digits is 18. It has a total of 8 prime factors and 24 positive divisors.

How do you solve prime factorization?

Prime Factorization Methods

1. Step 1: Divide the given number by the smallest prime number.
2. Step 2: Again, divide the quotient by the smallest prime number.
3. Step 3: Repeat the process, until the quotient becomes 1.
4. Step 4: Finally, multiply all the prime factors.

What are prime divisors?

Prime numbers are those integers greater than one whose only divisors are one and themselves (so whose only proper positive divisor is one). Several number theoretic functions are related to the divisors of n. For example, tau(n) (or ) is the number of divisors of n, and sigma(n) (or. ) is their sum.

How do you find the number of prime divisors of Pi?

The count of divisors will be (i 1 + 1) * (i 2 + 1) * … * (i k + 1). It can now be seen that there can only be one prime divisor for the maximum i and if N \% pi = 0 then (i + 1) should be prime. The primality can be checked in sqrt (n) time and the prime factors can also be found in sqrt (n) time.

How do you find the maximum number of prime divisors?

So find the maximum value of i for every prime divisor p such that N \% (pi) = 0. So the count of divisors gets multiplied by (i + 1). The count of divisors will be (i 1 + 1) * (i 2 + 1) * … * (i k + 1). It can now be seen that there can only be one prime divisor for the maximum i and if N \% pi = 0 then (i + 1) should be prime.

How do you sum the divisors of a number?

We need to find the divisors of the number first, and then sum them. Finding out if a number is a divisor of another number is pretty simple: Modulo – \% – returns the remainder of a division. 9 \% 2 = 1. 10 \% 3 = 1. However, we’ll need to know which numbers to check. We could just loop through every number up to our input: …but that’s too much.

How to check if a number is a prime number?

A naive approach will be to iterate for all numbers till N and check if the number divides N. If the number divides N, check if that number is prime or not. Add all the prime numbers till N which divides N. Below is the implementation of the above approach: // number is prime or not. // number is prime or not.