# 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 (i.e., 2,3,5,7, 11), the prime factorization is just a prime number. Other numbers are called composite numbers and have a minimum of two prime factors. For repeat, a prime number is a natural number that is divisible without a remainder by itself and by a unit, not by other natural numbers.

## Practice problems:

27 = 3 × 3 × 3198 = 2 × 3

^{2}× 11

1024 = 2

^{10}

19823 = 43 × 461

30258037 = 30258037

## Word problems and examples involving prime numbers

- How many

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. - Situation 78694

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. - 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. - Paul makes

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?

- 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

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1. - An example

An example is playfully for grade 6 from Math, and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: The student made a cuboid from a block of 16x18x48 mm of plasticine. What will be th - Dividing nuts

How many nuts do you have when dividing them between 2, 3, 4, 5, 6, 8, and 10 children? (smallest possible number)

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