Prime Factorization Calculator

Enter number

This calculator will find all of the prime factors of a natural number. Prime factorization of a number is the calculation of the primes that multiply together to give the original number. It is also known as prime decomposition.

The number 1 (one) is called a unit. It has no prime factors. When a number is a prime number (e.g., 2,3,5,7, 11), its prime factorization is simply the number itself. Other numbers are called composite numbers and have a minimum of two prime factors. To clarify, a prime number is a natural number that is divisible without a remainder only by itself and by 1, but not by any other natural numbers.

Practice problems:

27 = 3 × 3 × 3
198 = 2 × 3² × 11
1024 = 2¹⁰
19823 = 43 × 461
30258037 = 30258037

Word problems and examples involving prime numbers

• Rectangles - integers
  How many different rectangles with integer side lengths have an area S = 60 cm²?
• The land
  The owner wants to divide the land with dimensions of 220 m and 308 m into equally large square plots with the largest possible area. How long will one side of the plot be?
• Divisible without remainder
  Determine the number by which all these numbers, 22, 18, 25, 15, 35, and 10, are divisible without remainder. The number is greater than 1.
• The Iceland
  There is a geyser and a volcano in a nature reserve in Iceland. The geyser erupts regularly every 18 days, and clouds of smoke rise from the volcano every 40 days. How many times in the course of 9000 days will there be a situation where we can observe bo

• Divisible 79464
  The teacher wrote a number less than 50,000 on the board. The first student said: This number is divisible by 2 The second student said: This number is divisible by 3 And so on, down to the last one who claimed it was divisible by 13. Two in a row lied. W

more math problems »