Factor decomposition of a number
Powers
 
1. The powers in the prime factor decomposition of a number.

One of the applications of powers is the prime factor decomposition of a number.
Factorising a number is writing it as a product of prime factors.
- To work out the prime factor decomposition of a number we have to divide it by the first prime number we can.
- We have to  place the resulting quotient below the number.
- If it is possible we continue dividing that quotient successively by the same prime number.
- When we cannot divide it by that prime number, we divide it by the next possible prime number.
- And so forth until the final quotient is 1.
- Finally we write that number as a product of powers of prime factors.
 

This window shows how to do the prime factor decomposition of a number. To do this, type any natural number you like in the control box below the window and hit Enter.

To see how other numbers are decomposed, you can change the value of the number by using the triangles.

The largest number you can type is a 5-digit number.

On the right you can see the division with the prime factors and below the product of these prime factors written as powers.
If the exponent is 1, the exponent is not written.

Notice that any natural  number can be written as a product of powers whose bases are prime numbers.
2. Find the number from which this prime factor decomposition comes.
 
Do the product of these powers, type the number and hit Enter.

When clicking on Init the prime factor decomposition of another number will appear at random.
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  Eduardo Barbero Corral
 
Spanish Ministry of Education. Year 2007
 
 

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