10 Real-world Examples Of Prime Factorization To Understand It Better

We use various basic principles of math quite unknowingly in our daily life. Like, we are always using addition, subtraction, division, and multiplication everywhere- from restaurants to public transport. When a child learns numbers and basic math, they take time to identify each number while solving a problem. But when they grow up, they may not even need to read a whole problem but solve it at once. This happens because, with time, we become familiar with the concepts. Prime factorization is a similar example of this. Here, in this post, we have a bunch of real-life examples where we use prime factorization extensively, making our daily lives easier.

What is prime factorization?

It can be easy to understand if we say that prime factorization is actually reverse multiplication. For example, let’s take the number 32. We can say that it is the result of multiplication between 4 and 8. Now, we can further break the number 4 down into 2×2. Similarly, we can break down the number 8 and express it as 2x2x2. So, we can express 32 as a result of 2x2x2x2x2. This process is prime factorization, where we find the prime numbers that make up another number.

Another example might help you understand it better. Take 27, for example. We can say,

27= 3×9

But 9 is not a prime number. So, we have to break the number 9 into prime numbers.

9= 3×3

So, 27= 3x3x3

Thus, the prime factorization works.

How do we use prime factorization in real life?

In our day-to-day life, factorization is important and is used quite frequently too. The most common uses are money exchange, time estimation, calculating costs and estimations while traveling, etc. A more detailed description is here for you.

1. Planning to make some muffins? Count factorization in!

Prime factorization examples

Suppose you will have a few friends over for a sleepover at your place, and you plan to amaze them with the soft melt-in-your-mouth muffins. Including you, there will be six people. You check your muffin molds and find that you can make nine muffins at a time. So, either there will be three extra muffins, or you cannot give all of your friends two muffins each if they ask for more. But what if you get another mold of nine muffins? Then you will have 18 muffins. If you factorize 18, you will find,

18= 2x3x3=6×3

Now for six people, you have enough. Divide those muffins among your friends, with three for each of them. So, factorization eased your dividing of the muffins equally. 

2. Factorization in money exchange

Prime factorization examples

We are exchanging money so many times in a day, right? But little do we notice that we use factorization in every step. Here is an example. 

Take one dollar. We all know that 100 pennies make up a dollar. We also know that a dollar is equal to four quarters. Without realizing it, you did a factorization here.

100= 4×25

So, you can see four quarters, each of value 25, make 100 pennies or a dollar.

Here is another example for you. Suppose you need changes and you only have a twenty-dollar bill. While looking for a change, you can factorize 20. It will give you the following options:

20= 2×10

20= 1×20

20= 4×5

So, you can get four bills of five dollars, twenty bills of one dollar, or two bills of ten dollars.

3. Lining up and grouping

Prime factorization examples

Suppose you are a kindergarten teacher and one day at school, take the children to the playground. You need to group them and engage them in different playing activities. So, if you have 30 students in your class, you can factorize the number into;

30= 3×10


30= 3x2x5

So, if there are three swings in the playground, you can form ten groups with three children in each group and call one group to ride the swings once. Once these three children are done, you call the second group. This way, all 30 children get to swing. You get to satisfy every child with the help of factorization. 

If we take shipping service, for example, we will also find the use of factorization. Here is how. Suppose there are items weighing 100 lbs that need to be shipped somewhere. You can factorize 100 in the following ways-

100= 2×50



So, either you can take two packing boxes capable of carrying 50 lbs each, or you can choose four packing boxes of 25 lbs capability each. Either way, factorization comes in handy.

4. Conversion of units through factorization

Prime factorization examples

While solving a mathematical problem, you might often be asked to express something in a particular unit. Now, that is easy, but there might be a twist to the question if it asks to express the result as a product of primes. Let us make it clearer with an example. 

Say you wish to make a multicolor top for yourself and have two feet of a fabric of one color with you. Your tailor tells you that you need 40 inches of fabric to make a top. So, how much more do you need? To start with, you already have two feet, that is, 24 inches. So, you need to collect 16 more inches. By factorizing 16, you get-

16= 2x2x2x2

So, you can buy four more colors, each four inches long. Or you can buy fabric of two colors, each eight inches long. You can see how factorization makes finding options easier when you are in a fix. 

5. Time distribution

Prime factorization examples

The clock and the concept of time use prime factorization very prominently. A day is 24 hours, and each hour is divided into 60 minutes. So, let’s factorize 60.

60= 5x2x2x3

Looking at the clock on your wall, you will find five divisions between two numbers. Starting from 12, you will see that there are 12 increments in total, each of 5 minutes. So, you can understand how a clock is developed based on the prime factorization concept. 

You can express an hour into other forms also. Using the prime factors of 60, you can divide an hour into two parts of thirty minutes or four parts of 15 minutes each. So, if your doctor gives you a pill to take four times every day, you will need to factorize 24 hours into-

24= 2x2x2x3

That means you must have one of your pills every four hours. This is how prime factorization is used in time management also.

6. Driving somewhere far? Factorization calculates your hours

Suppose you reside in San Francisco and plan to visit the American Influencer Award show in Los Angeles. The distance between the two is around 380 miles. So, if you are driving to LA, you need to plan how long it will take you to reach there, whether you have to halt somewhere in the middle, etc. It will take around six hours if you drive an average of 65 miles per hour. You actually use factorization when you do this calculation. The traveling plan is yet another real-life example where you implement prime factorization. 

7. Factorization is the base of solving the Kenken puzzle.

Kenken is overtly popular in today’s times. You can even play it on New York Times online site. But while you play with the numbers and solve the puzzle, you might think you are simply using the functions mentioned in the blocks. In reality, you are using prime factorization extensively. In a Kenken puzzle, you break down the sums given into unique numbers. This very act of breaking down is the prime factorization or multiple factorizations. 

8. Workload distribution also involves factorization.

Prime factorization examples

Suppose you have a small painting business and five regular employees working with you. You suddenly get a huge order and a crunch deadline where you have to paint the indoors of a two-storied cafe. How do you manage it? Firstly, you know your employees and their levels of efficiency and skill. If one can do a job in six hours, maybe another employee can do the same in four. Again, someone else might take eight hours to do it. So, you can factorize their times and estimate who would take how much time to finish which part of the cafe. This way, you can meet the deadline and do a smart job. The way you do the math is nothing but simple prime factorization and other operations like H.C.F. and L.C.M.

9. Factorization in coding and cryptography

Prime factorization examples

In addition to the above list, prime factorization is also used in technological fields. Coders use prime factorization to create unique codes in cryptography to protect and secure information. Using this, they determine which numbers to use as code so that it becomes unique and easy for the system to process simultaneously. 

10. Factorization in gaming

Prime factorization examples

Video games or computer games that involve playing dice on-screen use prime factorization. With factorized programming, every time you click or tap to play the dice, it takes a certain number of turns and gives you a result.

Wrapping up

Prime factorization is used almost everywhere in our daily life. If a child is made familiar with these real-life examples, they can overcome any fear of it from a very early time. Good factorization skills can help an adult solve real-life problems without much hassle. We hope we have helped you understand prime factorization by heart with the above examples.

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