GCF Calculator — Greatest Common Factor & HCF Studio
Find Greatest Common Factor • Highest Common Factor (HCF) • Greatest Common Divisor (GCD) • Detailed Educational Steps
Greatest Common Factor Suite
Supports up to 100 numbers. Enter any numbers below 1 Billion to calculate.
Step-by-Step Mathematical Proofs
Understand how the GCF is computed using two standard educational methods.
Method 1: Listing Factors
Write down all positive factors for each number. Find the largest factor shared by all numbers.
Method 2: Prime Factorization
Decompose each number into its prime components. Identify the common prime factors and multiply their lowest powers.
GCF Quick Reference Sheet
Click any row to load the values into the analyzer.
| Number Pair / Set | GCF Result | Classification | Action |
|---|---|---|---|
| 12, 18 | 6 | Even Divisor | |
| 24, 36 | 12 | Even Divisor | |
| 15, 20 | 5 | Odd Divisor | |
| 32, 48 | 16 | Even Divisor | |
| 14, 28, 42 | 14 | Even Divisor | |
| 25, 75 | 25 | Odd Divisor | |
| 10, 20, 30 | 10 | Even Divisor | |
| 9, 27 | 9 | Odd Divisor | |
| 11, 13 | 1 | Coprime Set | |
| 60, 90 | 30 | Even Divisor |
Overview & Capabilities
Welcome to the Greatest Common Factor (GCF) Studio. This professional math suite calculates the GCF (also known as HCF or GCD) of any set of positive integers. It features instant multi-number solvers, comparative factor listings, prime factorization models, and local query history logs.
How to Use
Key Features
Tips & Best Practices
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Frequently Asked Questions
Q What is the Greatest Common Factor (GCF)?
The Greatest Common Factor (GCF) of two or more non-zero integers is the largest positive integer that divides all of the numbers perfectly without leaving a remainder. For example, the GCF of 12, 18, and 30 is 6.
Q What is the difference between GCF, HCF, and GCD?
There is no difference; they are different terms for the exact same mathematical concept. GCF stands for Greatest Common Factor, HCF stands for Highest Common Factor, and GCD stands for Greatest Common Divisor.
Q How does the Euclidean Algorithm work?
The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers. It is based on the principle that the GCD of two numbers also divides their difference. Iteratively, we replace the larger number by its remainder when divided by the smaller number, until the remainder is zero. The last non-zero divisor is the GCF.
Q What does "relatively prime" (coprime) mean?
Two or more numbers are relatively prime (or coprime) if their only common positive factor is 1. That is, their GCF is 1. For example, 8 and 15 share no common factors other than 1, so they are coprime.
Q How do you find GCF using Prime Factorization?
To find the GCF of a set of numbers using prime factorization, you first find the prime factors of each number. Next, identify the prime factors common to all numbers. Finally, multiply the lowest power of each common prime factor. For 24 (2³ × 3¹) and 36 (2² × 3²), the common prime factors are 2 and 3. The minimum power of 2 is 2², and of 3 is 3¹. Thus, GCF = 2² × 3¹ = 12.