Prime Factorization Calculator
Find prime factors, GCF, LCM, and check if numbers are prime step-by-step. Learn number theory with instant feedback. Perfect for KS3 and GCSE maths.
Step-by-step learning with explanations
Prime Calculator
Find prime factors, GCF, and LCM
Select an operation and enter a number, then click Calculate
Understanding Prime Numbers
A prime number is a number greater than 1 that has exactly two factors: 1 and itself. Prime numbers are the building blocks of all other numbers - every number can be expressed as a product of primes.
Prime factorization breaks down a number into its prime components. For example, 60 = 2² × 3 × 5. This is fundamental for finding GCF and LCM, simplifying fractions, and solving number problems.
Key Concepts
GCF vs LCM Explained
GCF (Greatest Common Factor)
Also called HCF (Highest Common Factor)
Uses COMMON prime factors only
Takes MINIMUM exponents
LCM (Least Common Multiple)
Smallest number divisible by both
Uses ALL prime factors
Takes MAXIMUM exponents
Example: GCF & LCM of 24, 36
24 = 2³ × 3¹
36 = 2² × 3²
GCF = 2² × 3¹ = 12, LCM = 2³ × 3² = 72
How It Works
Select Operation
Choose Prime Factorization, GCF, LCM, Prime Check, or Find Factors.
Enter Numbers
Type your number(s). For GCF/LCM, enter multiple numbers.
Click Calculate
See the result with detailed step-by-step working.
Learn or Get Answer
Learn Mode teaches each step; Quick Mode gives instant results.
First 20 Prime Numbers
Note: 1 is NOT prime (it only has one factor), and 2 is the only even prime.
Frequently Asked Questions
What is prime factorization?
Breaking down a number into a product of prime numbers. For example, 60 = 2² × 3 × 5. Every composite number has a unique prime factorization.
How do I find the GCF of two numbers?
Find the prime factorization of each number, identify common prime factors, and multiply them using the smallest exponent of each.
How do I find the LCM of two numbers?
Find the prime factorization of each number, list all prime factors, and multiply using the largest exponent of each prime.
What is the difference between GCF and LCM?
GCF is the largest number dividing both evenly; LCM is the smallest number both divide into evenly. GCF uses min exponents; LCM uses max exponents.
How do I know if a number is prime?
A prime has exactly two factors: 1 and itself. Check by dividing by primes up to the square root. Remember: 1 is NOT prime, and 2 is the only even prime.
Is this suitable for GCSE maths?
Yes! Covers all GCSE number theory topics including prime factorization, GCF/HCF, LCM, factor trees, and index notation with step-by-step working.
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