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HCF Calculator

Enter numbers to get their highest common factor, with the working.

Find
Positive whole numbers separated by commas or spaces.
Try:

Greatest common factor

gcd⁡(126, 198, 270)=18\gcd(126,\ 198,\ 270) = 18gcd(126, 198, 270)=18

Prime factorization table

Number222333555777111111
12612010
19812001
27013100
GCF (smallest)12000
LCM (largest)13111

The cells are exponents. The GCF takes the smallest exponent in each column, the LCM the largest.

Step by step

  1. 1Prime factorization
    126, 198, 270126,\ 198,\ 270126, 198, 270
    ↓
    126=2×32×7198=2×32×11270=2×33×5\begin{aligned}126 &= 2 \times 3^{2} \times 7\\198 &= 2 \times 3^{2} \times 11\\270 &= 2 \times 3^{3} \times 5\end{aligned}126198270​=2×32×7=2×32×11=2×33×5​

    Write every number as a product of primes.

  2. 2GCF: smallest power of each prime
    21×32×50×70×1102^{1} \times 3^{2} \times 5^{0} \times 7^{0} \times 11^{0}21×32×50×70×110
    ↓
    2×32=182 \times 3^{2} = 182×32=18

    Take only the primes that all the numbers share, each to its lowest power.

  3. 3LCM: largest power of each prime
    21×33×51×71×1112^{1} \times 3^{3} \times 5^{1} \times 7^{1} \times 11^{1}21×33×51×71×111
    ↓
    2×33×5×7×11=207902 \times 3^{3} \times 5 \times 7 \times 11 = 207902×33×5×7×11=20790

    Take every prime that appears anywhere, each to its highest power.

  4. 4Euclidean algorithm for 126 and 198
    198=1×126+72126=1×72+5472=1×54+1854=3×18+0\begin{aligned}198 &= 1 \times 126 + 72\\126 &= 1 \times 72 + 54\\72 &= 1 \times 54 + 18\\54 &= 3 \times 18 + 0\end{aligned}1981267254​=1×126+72=1×72+54=1×54+18=3×18+0​
    ↓
    gcd⁡(126, 198)=18\gcd(126,\ 198) = 18gcd(126, 198)=18

    Divide the larger by the smaller, then repeat with the divisor and the remainder. The last non-zero remainder is the GCF.

  5. 5Euclidean algorithm for 18 and 270
    270=15×18+0\begin{aligned}270 &= 15 \times 18 + 0\end{aligned}270​=15×18+0​
    ↓
    gcd⁡(18, 270)=18\gcd(18,\ 270) = 18gcd(18, 270)=18

    Divide the larger by the smaller, then repeat with the divisor and the remainder. The last non-zero remainder is the GCF.

  1. Tools
  2. Mathematics
  3. LCM and GCF Calculator
  4. HCF Calculator

About HCF Calculator

This HCF calculator finds the highest common factor, the same thing as the GCF or GCD, for up to ten whole numbers, with the prime factor and division methods. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The page opens on 126, 198 and 270. Their prime factorizations are 2 × 3² × 7, 2 × 3² × 11 and 2 × 3³ × 5. The shared primes with the smallest powers are 2 × 3² = 2 × 3^2, so the HCF is 18.

HCF is the term used in British, Indian and many other exam systems, with the common-division ladder as the usual school method. The LCM, which exam questions often ask for alongside, is shown too.

How to use HCF Calculator

  1. 1Choose LCM and GCF, LCM only or GCF only.
  2. 2Type two to ten positive whole numbers separated by commas or spaces.
  3. 3Read the answer at the top. It updates as you type.
  4. 4Check the prime exponent table: the GCF uses the smallest exponents and the LCM the largest.
  5. 5Open the steps for the Euclidean algorithm and, for two numbers, the link lcm = a × b ÷ gcd.

Features

  • LCM and GCF (GCD, HCF) of 2 to 10 numbers at once.
  • Prime factorization method with an exponent table.
  • Euclidean algorithm shown division by division.
  • Coprime detection.
  • Numbers of up to 24 digits, computed exactly with big integers.
  • Separate LCM-only and GCF-only views.
  • Step list in KaTeX with a copy button for the LaTeX.

HCF

The HCF is the product of the common prime factors to their lowest powers.

HCF(126, 198, 270) = 2 × 3² = 18

Worked examples

  • HCF of 126, 198 and 270 → gives 18

    LCM of the same numbers is 20790.

  • HCF and LCM of 12 and 18 → gives HCF 6, LCM 36

    HCF × LCM = 6 × 36 = 216 = 12 × 18.

Privacy: how it works

  • Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.

Tips

  • To add fractions, use the LCM of the denominators as the common denominator, which keeps the numbers small.
  • To simplify a fraction, divide top and bottom by their GCF in one step.
  • If the GCF of two numbers is 1, their LCM is just their product.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Numbers are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

Is HCF the same as GCF?

Yes. HCF, GCF and GCD are three names for the greatest number that divides all the given numbers.

How are HCF and LCM related?

For two numbers, HCF × LCM = the product of the numbers.

More LCM and GCF Calculator pages

  • LCM and GCF CalculatorEnter two to ten whole numbers to get their least common multiple and greatest common factor, with the working.
  • LCM CalculatorEnter two to ten numbers to get their least common multiple.
  • GCF CalculatorEnter two to ten numbers to get their greatest common factor.
  • GCD CalculatorEnter numbers to get the greatest common divisor, with every Euclidean step.

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