Prime Factorization Formula
Let us first define prime factorization before learning the prime factorization formula. It's a method of representing a number as the sum of its prime factors. "Every composite number can be factorised as a product of primes, and this factorization is unique, aside from the order in which the prime factors occur," says the fundamental theorem of arithmetic. The prime factorization formula aids in the discovery of any number's prime factorization.
Any composite number can be expressed as the product of powers of prime numbers, and this method of expressing the composite number as a product is known as prime factorization. Any number's prime factorization formula is as follows: You can get all Maths formulas on one-page visit the Maths Formulas section of HT.
N = Xa × Yb × Zc
where,
- N = Any number
- X, Y, and Z = Prime factors of number N
- a, b, and c = exponents of prime factors X, Y, and Z respectively
To find the prime factorization of any number, use the following method and formulas:
- Division Method: The steps for calculating a number's prime factors are similar to those for discovering any number's factors.
- To get the least prime factor of a number, start by dividing it by the smallest prime number, such as 2, then 3, 5, and so on.
- Divide the result by the smallest prime number once more.
- Repeat the method until the quotient, after repeated division, equals one.
- Finally, represent the number as the sum of all prime factors.
- Factor Tree Method: Create a tree to represent the number.
- As the root, keep the number in the centre.
- Divide the number by the smallest prime factor and express the factor as a single branch number.
- Rep the above procedure for the quotient obtained in the other branch until you get 1 as the factor for the remaining number.
- Each of the tree's branches will eventually reach a prime number.
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