Math

HCF Calculator

Find the Highest Common Factor (HCF)

The Highest Common Factor (HCF) — also known as the Greatest Common Divisor (GCD) — is the largest number that divides two integers evenly. This calculator finds the HCF using prime factorization and displays a Venn diagram of shared prime factors.

Prime Factorization Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Highly Composite Number

Factor 360, a highly composite number with many divisors.

Key values: 360 = 2^3 x 3^2 x 5 · 24 divisors · phi(360) = 96

Large Prime

Check if 7919 is prime (it is -- the 1000th prime number).

Key values: 7919 is prime · 2 divisors · phi(7919) = 7918

GCD and LCM

Compute the GCD and LCM of 84 and 120.

Key values: 84 = 2^2 x 3 x 7 · 120 = 2^3 x 3 x 5 · GCD = 12, LCM = 840

Documentation

This calculator is also known as HCF Calculator.

Read the complete guide

HCF vs GCD

HCF (Highest Common Factor) and GCD (Greatest Common Divisor) are the same thing — different names used in different countries. The UK, India, and Australia use HCF; the US and most of Europe use GCD.

Examples

HCF of 48 and 180

Simplify the fraction 48/180

48 = 2⁴ × 3, 180 = 2² × 3² × 5. HCF = 2² × 3 = 12. Divide both by 12: 48/180 = 4/15.

Key takeaway: The HCF tells you the largest number you can divide both numerator and denominator by.

Using the HCF

The HCF is essential for simplifying fractions and solving divisibility problems.

To simplify a fraction, divide numerator and denominator by their HCF
If HCF = 1, the numbers are coprime (the fraction is already in lowest terms)
Use the Venn diagram to see which prime factors are shared at a glance

Frequently Asked Questions about HCF Calculator

What is the HCF?

The Highest Common Factor (HCF) is the largest positive integer that divides two or more integers without a remainder. It is the same as the GCD (Greatest Common Divisor).

How do I find the HCF using prime factorization?

Factor both numbers into primes. The HCF is the product of each shared prime raised to the smaller of the two exponents.

What is the relationship between HCF and LCM?

HCF(a,b) × LCM(a,b) = a × b. You can find one from the other using this identity.

Specialized Calculators

Choose from 5 specialized versions of this calculator, each optimized for specific use cases and calculation methods.

Visualization

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Factor Tree Calculator | Visual Prime Factorization

Visualize prime factorization as an interactive factor tree diagram.

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Mode

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GCD and LCM Calculator | Greatest Common Divisor

Find the GCD and LCM of two integers using prime factorization with a Venn diagram.

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Purpose

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Primality Tester | Is This Number Prime?

Instantly check if any integer is prime or composite and see its full factorization.

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Divisor Calculator | Count and List All Divisors

Find all divisors of an integer, count them (d(n)), and compute their sum (\u03C3(n)).

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Euler\u2019s Totient Calculator | \u03C6(n) Function

Compute Euler\u2019s totient \u03C6(n) \u2014 the count of integers coprime to n. Used in RSA cryptography.

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