Prime Factorization Calculator

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
Determine 82852
The fan club has 275 members. Some members went to the match by train. Determine how many members rode when they could fill the wagons with either 60 or 80 seats.
Exactly divisibled
Find the least number that can be divided exactly by all the even numbers between 10 and 20

Three numbers
The product of three natural numbers is 600. If we reduced one factor by 10, the product would decrease by 400. If we increased one factor by 5 instead, the product would increase to twice the original value. Which three numbers have this property?
Motorcycles 4313
Three racing motorcycles drive at different speeds on the autodrome. One motorcycle can go around the circuit in 2 minutes, the second in 4 minutes, and the third in 7 minutes. If all three bikes enter the race track simultaneously, how long before they a
Workbooks 7701
Determine the smallest possible number of workbooks divided into stacks of 6, 8, 9, or 10.
Plasticine cuboid
Paul makes a cuboid of plasticine with sides 5 cm, 2 cm, and 5 cm. How many such cuboids will he need to form a cube?
In a forest meadow
The students planted 280 spruces and 60 pines on forest traps. Express the ratio of the number of planted pines to the number of planted spruces in the smallest possible natural numbers.
Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles
Prime factors
Write 98 as a product of prime factors.
Reminder and quotient
Numbers A = 135 and B = 315 are given. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1.