# 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

- Determine 70224

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. - 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? - 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. - 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 - 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 - Square room

What is the size of the smallest square room, which can pave with tiles with dimensions of 55 cm and 45 cm? How many are such tiles needed? - Reminder and quotient

There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S and D:S are with the remainder of 1. - Rectangles 70304

How many rectangles with side lengths expressed in natural numbers have an area of 96 cm²? - Steps

Peter makes steps long 70 cm, John 45 cm long. After how many meters do their footsteps meet? - Susan 3

Susan has 90 sweets, 36 chocolates, and 60 jellies. She wants to pack the items equally into goodie bags without any items left over. How many bags will she pack maximum? How many sweets, chocolates, and jellies will be in one bag? - Tiles

It is given an area of 5m x 4m. One tile is 40 x 40 cm. How many tiles are needed in an area of 5 m x 4 m? And how many tiles need to be cut (if the tiles can't fall exactly)? - John Smith

John Smith is reading a 435-page novel. If he reads the same number of pages per day and the number is a prime number greater than 10, how many pages per day will he read? - Oranges

The mother divided her three children's oranges in a ratio of 6:5:4. Two children gave 45 oranges. How many oranges were there? - Pegs

From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?

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