Prime factorization can be used to represent a number as a product of its prime components. A prime number has only one and the number itself as components. As an example, consider the number 30. Although we know that 30 = 5 6 is a prime number, 6 is not. The number 6 can also be factored as 2 3 since 2 and 3 are prime integers. As a result, 30’s prime factorization is 2 3 5, and all of its factors are prime numbers.
What Is Prime Factorization and What Does It Mean?
Prime numbers are those with only one element, one, and the number itself.
Definition of Prime Factorization
Prime factorization is the process of breaking down a number into prime numbers that help construct the number when multiplied. To put it another way, prime numbers are multiplied with the multiples to get the original number.
What are Prime Factors and Factors?
The numbers that are multiplied to acquire the original number are called factors of a number. 4 and 5 are factors of 20, i.e., 4 5 = 20, whereas prime factors of a number are prime numbers multiplied to produce the original number. For example, the prime factors of 20 are 2, 2, and 5, therefore 2 2 5 Equals 20.
Prime factorization is similar to factoring a number, except that it only considers prime numbers as factors (2, 3, 5, 7, 11, 13, 17, 19, and so on). As a result, factors that divide the original number fully and cannot be broken into other factors can be defined.
Prime Factorization Techniques
The prime factorization of a number can be done in a variety of ways. The following are the most often used prime factorization methods:
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Factor tree approach for prime factorization
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The division method is used to factorise prime factors.
Factor Tree Method for Prime Factorization
The factor tree approach involves finding a number’s factors and then factorising those numbers until we reach prime numbers. The steps below are used to determine a number’s prime factorization using the factor tree method:
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Step 1: Place the number on top of the factor tree in step one.
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Step 2: Then, as the tree’s branches, put down the relevant pair of components.
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Repeat step 2.
Using the Division Method to Prime Factorize
By dividing a huge integer by prime numbers, the division technique may be used to identify the prime factors.
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Step 1: Divide the number by the lowest prime number, making sure that the smallest prime number entirely divides the number.
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Step 2: Divide the quotient obtained in step 1 by the lowest prime number once again.
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Step 3: Continue with step 2 until the quotient equals one.
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Step 4: Finally, multiply all of the divisors’ prime factors.
Prime factorization and cryptography
Cryptography is a code-based way of securing data. Prime factorization is useful for coders who want to make a unique code out of numbers that isn’t too large for computers to store or process rapidly.
LCM and HCF Prime Factorization
It is a method of calculating the number of factors that make up The prime factorization method is used to identify the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two integers. To accomplish so, we must first factorise both integers into prime factors.
Conclusion
This was all about the concept of prime factorisation. If you are planning to learn the concept then join the Cuemath classes today and enjoy it with the right experts.
