Prime Factorization Calculator
Here is the answer to questions like: Find the prime factorization of 210 using exponents or is 210 a prime or a composite number?
Use the Prime Factorization tool above to discover if any given number is prime or composite and in this case calculate the its prime factors. See also in this web page a Prime Factorization Chart with all primes from 1 to 1000.
What is prime factorization?
Definition of prime factorization
The prime factorization is the decomposition of a composite number into a product of prime factors that, if multiplied, recreate the original number. Factors by definition are the numbers that multiply to create another number. A prime number is an integer greater than one which is divided only by one and by itself. For example, the only divisors of 7 are 1 and 7, so 7 is a prime number, while the number 72 has divisors deived from 23•32 like 2, 3, 4, 6, 8, 12, 24 ... and 72 itself, making 72 not a prime number. Note the the only "prime" factors of 72 are 2 and 3 which are prime numbers.
Prime factorization example 1
Let's find the prime factorization of 72.
Solution 1
Start with the smallest prime number that divides into 72, in this case 2. We can write 72 as:
72 = 2 x 36
Now find the smallest prime number that divides into 36. Again we can use 2, and write the 36 as 2 x 18, to give.
72 = 2 x 2 x 18
18 also divides by 2 (18 = 2 x 9), so we have:
72 = 2 x 2 x 2 x 9
9 divides by 3 (9 = 3 x 3), so we have:
72 = 2 x 2 x 2 x 3 x 3
2, 2, 2, 3 and 3 are all prime numbers, so we have our answer.
In short, we would write the solution as:
72 = 2 x 36
72 = 2 x 2 x 18
72 = 2 x 2 x 2 x 9
72 = 2 x 2 x 2 x 3 x 3
72 = 23 x 32 (prime factorization exponential form)
Solution 2
Using a factor tree:
- Procedure:
- Find 2 factors of the number;
- Look at the 2 factors and determine if at least one of them is not prime;
- If it is not a prime factor it;
- Repeat this process until all factors are prime.
See how to factor the number 72:
Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have
72 = 2 x 2 x 2 x 3 x 3
72 = 23 x 32 (prime factorization exponential form)
Note that these dividers are the prime factors. They are also called the leaves of the factor tree.
Prime factorization example 2
See how to factor the number 588:
Taking the left-hand numbers and the right-most number of the last row (dividers) an multiplying then, we have
588 = 2 x 2 x 3 x 7 x 7
588 = 22 x 3 x 72 (prime factorization exponential form)
Prime Factorization Chart 1-1000
Prime Factorization Calculator
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