Mathematical Operations With Prime Numbers

Prime Numbers. 8 Free Online Calculators Available.


All the mathematical operations are performed automatically.

All the operations and the results are explained in detail, step by step.

All the online calculators are free to use.

They are listed below:


1. Prime factorization: Check whether numbers are prime. Composite numbers prime factorization (decomposing, breaking numbers down to prime factors). Write them as a product of prime factors, in exponential notation. Online calculator


Latest factored numbers (latest prime factorizations)

2. Calculate GCF (HCF, GCD), the greatest (highest) common factor (divisor). Online calculator


The latest calculated greatest (highest) common factors (divisors), gcf (hcf, gcd)

3. Calculate LCM, the least common multiple of numbers. Online calculator


The latest calculated values of the "least common multiple", LCM

4. Fractions reducing (simplifying) to lowest terms. Online calculator


Latest fractions reduced (simplified) to the lowest terms

5. Divisibility: Tell and explain whether a number is divisible by another. Online calculator


The latest numbers that were checked to see whether they are divisible or not

6. All the factors (divisors) of one or two numbers. Online calculator


Latest calculated factors (divisors)

7. Are the numbers coprime (relatively prime, prime to each other)? Online calculator


Coprime numbers or not (relatively prime, prime to each other or not)? Latest operations

8. Parity: even or odd integer numbers? Online calculator


Latest numbers tested on parity: even or odd?

parity (9,699,710) = even Nov 25 19:10 UTC (GMT)
parity (37,071) = odd Nov 25 19:10 UTC (GMT)
parity (21,317) = odd Nov 25 19:10 UTC (GMT)
parity, see more...

Articles about prime numbers

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples

Prime numbers definition. Composite numbers

Positive integers that are only dividing by themselves and number 1 are called prime numbers.

A composite number is a positive integer that has at least one positive divisor other than 1 and the number itself. A composite number is also any positive integer larger than 1 that is not a prime number.

  • 2 is divisible only by 2 and 1, so 2 is a prime number
  • 3 is divisible only by 3 and 1, so 3 is a prime number
  • 5 is divisible only by 5 and 1, so 5 is a prime number
  • 13 is divisible only by 13 and 1, so 13 is a prime number

1 is not considered prime, so the first prime number is 2 (prime numbers list is starting with the number 2)

The fundamental theorem of arithmetic says that every integer larger than 1 can be written as a product of one or more prime numbers in a way that is unique, except for the order of the prime factors. Prime numbers are thus the basic building blocks of all numbers. If 1 were admitted as a prime, number 15 for example could be factored as 3 × 5 and 1 × 3 × 5; these two representations would be considered different prime factorizations of 15 (prime factorization into prime factors), so the statement of the theorem would have to be modified.
  • 4 is divisible by 4, 2 and 1, so 4 is not a prime number, it's a composite number; 4 = 22
  • 6 is divisible by 6, 3, 2 and 1, so 6 is not a prime number, it's a composite number; 6 = 2 × 3
  • 8 is divisible by 8, 4, 2 and 1, so 8 is not a prime number, it's a composite number; 8 = 23
  • 9 is divisible by 9, 3, and 1, so 9 is not a prime number, it's a composite number; 9 = 32

Examples of prime numbers, up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

EUCLID (300 B.C.) proved that as the set of natural or integer numbers is infinite, also the the set of prime numbers is infinite, with no largest prime number.

There is no known simple formula that sets apart all of the prime numbers from composites.