Prime Factorization
Prime Numbers
A Prime Number is a whole number, greater than 1, that can
be evenly divided only by 1 or itself. Read more about Prime
and Composite Numbers.
The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ...,
and we have a prime number chart
if you need more.
Factors
"Factors" are the numbers you multiply together to get
another number:
Prime Factorization
"Prime Factorization" is finding which prime numbers
you need to multiply together to get the original number.
Example 1
What are the prime factors of 12?
It is best to start working from the smallest prime number, which
is 2, so let's check:
12 ÷ 2 = 6
But 6 is not a prime number, so we need to factor it further:
6 ÷ 2 = 3
And 3 is a prime number, so:
12 = 2 × 2 × 3
As you can see, every factor is a
prime number, so the answer must be right - the prime factorization
of 12 is 2 × 2 × 3, which can also be written as 22
× 3
Example 2
What is the prime factorization of 147?
Can we divide 147 evenly by 2? No, so we should try the next prime
number, 3:
147 ÷ 3 = 49
Then we try factoring 49, and find that 7 is the smallest prime
number that works:
49 ÷ 7 = 7
And that is as far as we need to go, because all the factors are
prime numbers.
147 = 3 × 7 × 7 =
3 × 72
Another Method
We showed you how to do the factorization by starting at the smallest prime and working upwards, but sometimes it is easier to break a number down into any factors you can, then work those factor down to primes.
Example: What are the prime factors of 90?
Break 90 into 9 × 10
- The prime factors of 9 are 3 and 3
- The prime factors of 10 are 2 and 5
So the prime factors of 90 are 3, 3, 2 and 5
Why?
A prime number can only be divided by 1 or itself, so it cannot
be factored any further!
Every other whole number can be broken down into prime number factors.
 |
It is like the Prime Numbers are the basic building blocks of all numbers. |
This can be very useful when working with big numbers, such as in Cryptography.
Cryptography
Cryptography is the study of secret codes. Prime Factorization is very important to people who try
to make (or break) secret codes based on numbers.
That is because factoring very large numbers is very hard, and can take computers a long time to do.
If you want to
know more, the subject is "encryption" or "cryptography".
Unique
And here is another thing:
There is only one (unique!) set of prime factors for any number.
Example The prime factors of 330 are 2, 3, 5 and 11:
330 = 2 × 3 × 5 × 11
There is no other possible set of prime numbers that can be multiplied to make 330.
In fact this idea is so important it is called the Fundamental Theorem of Arithmetic.
Prime Factorization Tool
OK, we have one more method ... use our Prime Factorization Tool that can work out the prime factors for numbers up to
4,294,967,296.
|
Home
