Prime Factorization Calculator: Find Prime Factors with Steps

Q: 3. What is the prime factorization of 180?

The prime factorization of 180 is 2 x 2 x 3 x 3 x 5, or 22 x 32 x 5. This means that 2, 2, 3, 3, and 5 are the prime numbers that multiply to equal 180.

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How to Use the Prime Factorization Calculator with Examples

What is Prime Factorization Calculator?

A prime factorization calculator breaks any whole number into its prime number building blocks, instantly and step by step. You simply enter your number, and it displays all the prime factors as a multiplication.

This tool saves time compared to manual division or drawing factor trees, especially for large numbers. It helps you see every division, making concepts and number theory problems easy to visualize.

Formula Behind Prime Factorization Calculator

To find the prime factors of any positive integer greater than 1, divide continuously by the lowest possible prime (starting from 2, then 3, 5, etc.), each time saving the divisor when it fits exactly. Keep dividing by the same prime until it no longer divides evenly, and then move to the next prime, repeating until the result is 1. The original number equals the product of all the primes found.

Prime Factorization Table

Number	Prime Factorization	Steps (abbreviated)
12	2 × 2 × 3	12÷2=6, 6÷2=3, 3÷3=1
18	2 × 3 × 3	18÷2=9, 9÷3=3, 3÷3=1
24	2 × 2 × 2 × 3	24÷2=12, 12÷2=6, 6÷2=3, 3÷3=1
36	2 × 2 × 3 × 3	36÷2=18, 18÷2=9, 9÷3=3, 3÷3=1
48	2 × 2 × 2 × 2 × 3	48÷2=24...→3÷3=1
60	2 × 2 × 3 × 5	60÷2=30, 30÷2=15, 15÷3=5, 5÷5=1
72	2 × 2 × 2 × 3 × 3	72÷2=36...→3÷3=1
100	2 × 2 × 5 × 5	100÷2=50, 50÷2=25, 25÷5=5, 5÷5=1
120	2 × 2 × 2 × 3 × 5	120÷2=60...→5÷5=1
210	2 × 3 × 5 × 7	210÷2=105, 105÷3=35, 35÷5=7, 7÷7=1
180	2 × 2 × 3 × 3 × 5	180÷2=90...→5÷5=1
756	2 × 2 × 3 × 3 × 3 × 7	756÷2...→7÷7=1

Steps to Use Prime Factorization Calculator

Enter your number (from 2 up to 10,000,000,000) in the box above.
Click the "Calculate" button.
Read the list of prime factors and see each calculation step shown.

Why Use Vedantu’s Prime Factorization Calculator?

It provides instant, exact prime factors of any number, complete with stepwise explanations you can trust in exams. The mobile-friendly design ensures you can review or practice prime factorizations anytime, anywhere.

All outputs are presented with a detailed breakdown, making this tool ideal for learning or test prep. Vedantu’s calculator is reviewed by maths teachers and aligned with Indian curriculum, helping you confidently solve HCF, LCM, and more.

Applications of Prime Factorization Calculator

Prime factorization is essential for quickly finding HCF and LCM of numbers, simplifying fractions, and checking divisibility. Maths competitions and school exams often involve factoring challenges you can check with this tool.

It also has uses in coding (like cryptography), advanced topics in algebra, and even real-world problem-solving. Many competitive exams directly test your understanding of factors and multiples—skills built using this calculator.

Learn even more about prime numbers and factors on Vedantu. For related maths tools, check our HCF Calculator or explore Algebra Topics to build solid number theory foundations.

FAQs on Prime Factorization Calculator: Find Prime Factors with Steps

1. What is prime factorization?

Prime factorization is the process of finding the prime numbers that, when multiplied together, give the original number. It's a fundamental concept in number theory.
Prime numbers are whole numbers greater than 1 that are only divisible by 1 and themselves (e.g., 2, 3, 5, 7, 11).

2. How do you find the prime factors of a number?

To find the prime factors, repeatedly divide the number by the smallest prime number until you reach 1. The prime numbers used in the division are the prime factors. For example, to find the prime factors of 12, you would divide by 2 (getting 6), then 2 again (getting 3), and finally 3 (getting 1). Therefore, the prime factors of 12 are 2, 2, and 3. You can express this as 2 x 2 x 3 = 12.

3. What is the prime factorization of 180?

The prime factorization of 180 is 2 x 2 x 3 x 3 x 5, or 2² x 3² x 5. This means that 2, 2, 3, 3, and 5 are the prime numbers that multiply to equal 180.

4. How do I use a prime factorization calculator?

Typically, you enter the number you want to factorize into the calculator's input field and then click a 'Calculate' or similar button. The calculator will then display the prime factors and may show the steps involved. Vedantu's calculator provides a clear step-by-step process to understand the calculation.

5. What are the prime factors of 756?

The prime factorization of 756 is 2 x 2 x 3 x 3 x 3 x 7, or 2² x 3³ x 7. These are the prime numbers that multiply together to make 756.

6. What is the difference between factors and prime factors?

Factors are any numbers that divide evenly into a given number. Prime factors are factors that are also prime numbers. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The prime factors of 12 are 2 and 3.

7. Why is prime factorization important?

Prime factorization is crucial for simplifying fractions, finding the greatest common factor (GCF) and least common multiple (LCM) of numbers, and understanding various concepts in algebra and number theory. It's a building block for more advanced mathematical concepts.

8. How can I find the prime factors of a large number?

For large numbers, using a prime factorization calculator is the most efficient method. Manually finding prime factors for very large numbers can be extremely time-consuming. Vedantu's calculator can handle larger numbers, making the process much faster and easier.

9. What are some real-world applications of prime factorization?

Prime factorization has applications in cryptography (secure communication), coding theory (error correction), and various areas of mathematics. Understanding prime numbers and their factorization is essential for problem-solving in many mathematical fields.

10. How is prime factorization used to find the LCM and HCF?

To find the least common multiple (LCM) and highest common factor (HCF) of two or more numbers, you first find their prime factorizations. The LCM is found by taking the highest power of each prime factor present in the factorizations and multiplying them together. The HCF is found by taking the lowest power of each prime factor common to all the factorizations and multiplying them together.

11. Can I use this calculator for fractions?

No, this calculator is designed for whole numbers only. To find the prime factorization of a fraction, you would first need to simplify the fraction to its lowest terms and then factorize the numerator and denominator separately.