Prime Factorization Calculator
Any number can be factored using the prime factorization calculator. Simply enter the integer into our tool, and you'll get the prime factorization in a matter of seconds. To understand the entire procedure, you must first become acquainted with the most important factor. We'll move on to the difference between a prime factor and prime factorization once you've grasped that. Continue reading further modules to learn about what is meant by Prime Factorization, Different Methods to find Prime Factorization of a Number, Solved Examples on Prime Factorization for better understanding of the concept.
What is Meant by Prime Factorization?
In mathematics, prime factorization is the method to find the prime factors of the number.The original number can be obtained by multiplying the prime factors of the numbers. We know that a prime number is a number that is divisible by the number 1 and the number itself. The method called the prime factorization method is used to break down the whole number into its prime factors. The decomposition of a composite number into a product of prime numbers is known as prime factorization.
What is a Prime Factor?
Factors of a number that are prime numbers are known as prime factors. For example, suppose we want to find the factors of 40, that is, we want to know what whole numbers multiply to give you 40. We know that 4 * 10 = 40, 2 * 20 = 40 and 8 * 5 = 40. But notice that 4, 2, and 8 are not prime factors. The only prime factors of 40 are 2 and 5. You can also get these factors with the use of our prime factor calculator.
Methods to find Prime Factorization of a Number
There are several methods to find Prime Factorization of a Number and they are explained in detail below. They are as follows
- Trail Division
- Factor Tree Method
Prime Factorization of a Number using Trail Division
One type for finding the prime factors of a composite number is trial division. Trial division is one of the more basic routes, though it is highly monotonous. It includes testing each integer by dividing the composite number in question by the integer, and determining if, and how many times, the integer can divide the number evenly.
As a simple example, below is the prime factorization of 420 using trial division:
420 ÷ 2 = 210
210 ÷ 2 = 105
Since 105 is no longer divisible by 2, test the next integers. 105 cannot be evenly divided by 3. 4 is not a prime number. However, it can be divided into 5:
105 ÷ 5 = 21
Since 21 is a prime number, this concludes the trial division. Thus:
420 = 21 × 5 × 2 × 2
The products can also be written as:
420 = 21 × 5 × 22
This is essentially the "brute force" method for determining the prime factors of a number, and though 420 is a simple example, it can get far more tedious very swiftly.
Prime Factorization using Factor Tree Method
Set of factors for the given number which make branches of a factor tree can be written by us
- Obtain the factors of the given number.
- Place those factors on the tree and we would stop at the prime factors or prime numbers inorder to stop the infinite chain of same factors.
Example:
Find the prime factors of 56 by using the factor tree method?
Solution:
By seeing the image we can express the prime factors of 56 as 7x2x2x2.
Prime Factorization of Common Numbers
Prime factorization of 2: prime number
Prime factorization of 3: prime number
Prime factorization of 4: 2²
Prime factorization of 5: prime number
Prime factorization of 6: 2 × 3
Prime factorization of 7: prime number
Prime factorization of 8: 2³
Prime factorization of 9: 3²
Prime factorization of 10: 2 × 5
Prime factorization of 11: prime number
Prime factorization of 12: 2² × 3
Prime factorization of 13: prime number
Prime factorization of 14: 2 × 7
Prime factorization of 15: 3 × 5
Prime factorization of 16: 2⁴
Prime factorization of 17: prime number
Prime factorization of 18: 2 × 3²
Prime factorization of 19: prime number
Prime factorization of 20: 2² × 5
Prime factorization of 21: 3 × 7
Prime factorization of 22: 2 × 11
Prime factorization of 23: prime number
Prime factorization of 24: 2³ × 3
Prime factorization of 25: 5²
Prime factorization of 26: 2 × 13
Prime factorization of 27: 3³
Prime factorization of 28: 2² × 7
Prime factorization of 29: prime number
Prime factorization of 30: 2 × 3 × 5
Prime factorization of 31: prime number
Prime factorization of 32: 2⁵
Prime factorization of 33: 3 × 11
Prime factorization of 34: 2 × 17
Prime factorization of 35: 5 × 7
Prime factorization of 36: 2² × 32
Prime factorization of 37: prime number
Prime factorization of 38: 2 × 19
Prime factorization of 39: 3 × 13
Prime factorization of 40: 2³ × 5
Prime factorization of 41: prime number
Prime factorization of 42: 2 × 3 × 7
Prime factorization of 43: prime number
Prime factorization of 44: 2² × 11
Prime factorization of 45: 3² × 5
Prime factorization of 46: 2 × 23
Prime factorization of 47: prime number
Prime factorization of 48: 2² × 3
Prime factorization of 49: 7²
Prime factorization of 50: 2 × 5²
Prime factorization of 100: 2² × 5²
FAQs on Prime Factorization Calculator
1. What is prime factorization?
In Maths, the prime factorization (also known as Prime Integer Factorization) consists in writing a positive integer with a product of prime factors. This factorization is unique in that it exists for all numbers and can be used in a variety of ways.
2. How do you find a number's prime factorization?
We can find the Prime Factorization of a number by using various methods like Trial Division and Factor Tree.
3. What is the prime factorization of 46?
Prime factorization of 46 is 2x23.