108 LearnersLast updated on August 9th, 2025
Prime Factorization Formula
Prime factorization is the process of expressing a number as a product of its prime factors. In this topic, we will explore the concept of prime factorization and the formula used to find the prime factors of a number.
Understanding Prime Factorization Formula
Prime factorization involves breaking down a composite number into its prime components. Let’s learn how to apply the formula to determine the prime factors of a number.
Prime Factorization Formula Explained
The prime factorization of a number is finding the prime numbers that multiply together to make the original number.
The prime factorization formula is applied by continuously dividing the number by prime numbers until only 1 is left. The prime factors are the divisors used in this process.
Steps to Perform Prime Factorization
To find the prime factors of a number, follow these steps:
1. Start with the smallest prime number, which is 2.
2. Divide the number by 2 until it is no longer divisible by 2.
3. Move to the next smallest prime number (3, 5, 7, etc.) and repeat the division process.
4. Continue this process until the number is reduced to 1.
Example of Prime Factorization
Let’s perform the prime factorization of 60.
1. Divide 60 by 2: 60 ÷ 2 = 30 2. Divide 30 by
2: 30 ÷ 2 = 15
3 . Divide 15 by 3: 15 ÷ 3 = 5
4. 5 is a prime number, so we stop here.
Thus, the prime factorization of 60 is 2 × 2 × 3 × 5.
Importance of Prime Factorization
In mathematics, prime factorization is an essential tool for simplifying fractions, finding the greatest common divisors, and determining the least common multiples.
Understanding prime factorization helps in solving complex mathematical problems and enhances number theory skills.
Tips and Tricks for Prime Factorization
Students often find prime factorization challenging.
- Here are some tips and tricks to master it:
- Familiarize yourself with prime numbers up to 100 for quick reference.
- Use division shortcuts: if a number ends in an even digit, it is divisible by 2; if it ends in 0 or 5, it is divisible by 5.
- Practice with different numbers to build confidence and speed.
Common Mistakes and How to Avoid Them in Prime Factorization
Students often make errors during prime factorization. Here are some common mistakes and how to avoid them to master the skill.
Mistake 1
Starting with Non-Prime Numbers
Students may start dividing by numbers that are not prime.
Always begin with the smallest prime number, which is 2, to avoid errors.
Mistake 2
Incorrect Division
Errors can occur if the division is not performed accurately.
Double-check each division step to ensure correctness.
Mistake 3
Stopping Too Early
Students sometimes stop factorizing before reaching the last prime number.
Continue the process until the number is reduced to 1.
Mistake 4
Confusing Composite and Prime Numbers
Students often confuse composite numbers with prime numbers, leading to incorrect factorization.
Understanding the difference between them is crucial.
Mistake 5
Skipping Prime Numbers in Sequence
Skipping prime numbers during factorization can result in missed factors.
Follow the sequence of prime numbers systematically.
Examples of Problems Using Prime Factorization Formula
Problem 1
What is the prime factorization of 84?
The prime factorization of 84 is 2 × 2 × 3 × 7.
Explanation
To find the prime factorization, divide 84 by the smallest prime number:
84 ÷ 2 = 42 - 42 ÷ 2 = 21 - 21 ÷ 3 = 7
7 is a prime number.
So, the prime factorization is 2 × 2 × 3 × 7.
Problem 2
Find the prime factorization of 150.
The prime factorization of 150 is 2 × 3 × 5 × 5.
Explanation
To find the prime factorization, divide 150 by the smallest prime number:
150 ÷ 2 = 75 - 75 ÷ 3 = 25 - 25 ÷ 5 = 5
5 is a prime number.
So, the prime factorization is 2 × 3 × 5 × 5.
Problem 3
Determine the prime factorization of 98.
The prime factorization of 98 is 2 × 7 × 7.
Explanation
To find the prime factorization, divide 98 by the smallest prime number:
98 ÷ 2 = 49 - 49 ÷ 7 = 7 - 7 is a prime number.
So, the prime factorization is 2 × 7 × 7.
Problem 4
What is the prime factorization of 200?
The prime factorization of 200 is 2 × 2 × 2 × 5 × 5.
Explanation
To find the prime factorization, divide 200 by the smallest prime number:
200 ÷ 2 = 100 - 100 ÷ 2 = 50 - 50 ÷ 2 = 25 - 25 ÷ 5 = 5
5 is a prime number.
So, the prime factorization is 2 × 2 × 2 × 5 × 5.
Problem 5
Find the prime factorization of 45.
The prime factorization of 45 is 3 × 3 × 5.
Explanation
To find the prime factorization, divide 45 by the smallest prime number:
45 ÷ 3 = 15 - 15 ÷ 3 = 5
5 is a prime number.
So, the prime factorization is 3 × 3 × 5.
FAQs on Prime Factorization Formula
1.What is prime factorization?
2.Why is prime factorization important?
3.How do I find prime factors of a number?
4.Can every number be factorized into primes?
5.What are some common prime numbers?
Glossary for Prime Factorization Concepts
- Prime Number: A number greater than 1 that has no divisors other than 1 and itself.
- Composite Number: A number that has more than two distinct positive divisors. Greatest
- Common Divisor: The largest positive integer that divides each of the integers without a remainder.
- Least Common Multiple: The smallest positive integer that is divisible by each of the given numbers.
- Prime Factorization: The expression of a number as a product of its prime numbers.
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
