09 / Mathematics
Free Math Calculators with Steps
Math calculators that show the working, not just the answer. Start with the GCF calculator, which solves the same problem three ways so you can follow the method your class uses. Free, no sign-up, and more calculators on the way.
GCF Calculator
Find the greatest common factor of up to 10 numbers and see every step, by listing factors, by prime factorization or with the Euclidean algorithm. It also gives the LCM and simplifies a fraction for you.
Use tool →LCM Calculator
The least common multiple of a set of numbers, worked out step by step with prime factors and the GCF shortcut.
In developmentPrime Factorization Calculator
Break any whole number into its prime factors, shown as a factor tree and in index form.
In developmentFraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, with the answer reduced to its simplest form.
In developmentPercentage Calculator
Percent of a number, percentage change and reverse percentages, with the formula shown next to each answer.
In developmentAlgebra Equation Solver
Solve linear and quadratic equations and follow each rearrangement, one line at a time.
In developmentStart here
Why use a math calculator that shows steps?
An answer on its own does not help much when you have to show your working in a test. Each calculator here is built to explain how it got there.
For students
Check homework, then compare your working line by line with the calculator's to find exactly where a mistake crept in. Seeing the same problem solved three ways also makes it easier to pick the method you find clearest.
For teachers and tutors
Produce a fully worked example for any pair of numbers in seconds, for a worksheet, a board demo or an answer key, and show the class how listing factors and the Euclidean algorithm reach the same result.
For everyday use
The GCF turns up outside the classroom more than people expect: reducing a recipe or a ratio, working out a screen aspect ratio, or splitting items into equal groups with nothing left over.
The calculators follow the standard methods taught in school syllabuses, so the working matches what a teacher expects to see. Use them to check and understand your work, not in place of doing it.
Worked example
One problem, three methods: the GCF of 48 and 72
Teachers ask for different methods at different stages, so the GCF Calculator shows all three. Here is what each one looks like on the same pair of numbers. All three land on 24, which is the point: the method changes, the answer does not.
| Method | The working | Best for |
|---|---|---|
| Listing factorsearly grades | 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Largest number in both lists: 24 | Small numbers, and seeing what a factor actually is |
| Prime factorizationmiddle school | 48 = 24 × 3 72 = 23 × 32 Lowest power of each shared prime: 23 × 3 = 24 | Getting the GCF and the LCM from one piece of working |
| Euclidean algorithmhigh school and beyond | 72 = 1 × 48 + 24 48 = 2 × 24 + 0 Last non-zero remainder: 24 | Large numbers, where listing factors would take pages |
The same factorization gives the LCM too: take the highest power of each prime, 24 × 32 = 144. As a check, 24 × 144 = 3,456, which is exactly 48 × 72.
FAQ
Free Math Calculators with Steps: FAQs
Are these math calculators free?
Yes. Every calculator on Calcxi is free, with no account, no email and no limit on how many problems you solve. Ads on the page pay for the site.
What is the greatest common factor (GCF)?
The greatest common factor of two or more whole numbers is the largest number that divides all of them with no remainder. For 12 and 18 the common factors are 1, 2, 3 and 6, so the GCF is 6.
Are GCF, GCD and HCF the same thing?
Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) are three names for the same number. GCF is common in US schools, HCF in the UK and India, and GCD in higher maths and programming. The GCF Calculator answers all three.
How do you find the GCF using prime factorization?
Write each number as a product of primes, then multiply the primes they share, each at its lowest power. For 48 and 72: 48 = 2 × 2 × 2 × 2 × 3 and 72 = 2 × 2 × 2 × 3 × 3. They share three 2s and one 3, so the GCF is 2 × 2 × 2 × 3 = 24.
What is the Euclidean algorithm?
A method for finding the GCF by repeated division. Divide the larger number by the smaller, replace the larger number with the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF. It is the fastest method for big numbers because the numbers shrink quickly at every step.
What is the difference between GCF and LCM?
The GCF is the largest number that divides into all your numbers. The LCM, or least common multiple, is the smallest number that all of them divide into. For 4 and 6 the GCF is 2 and the LCM is 12. You use the GCF to simplify, and the LCM to find a common denominator.
How are GCF and LCM related?
For any two positive whole numbers, GCF × LCM = the product of the two numbers. So once you know the GCF you can get the LCM by dividing the product by it: for 48 and 72, 3,456 ÷ 24 = 144. This shortcut works for two numbers only, not for three or more.
How do I simplify a fraction using the GCF?
Divide the top and the bottom by their GCF. For 36/48 the GCF is 12, and 36 ÷ 12 = 3 while 48 ÷ 12 = 4, so 36/48 simplifies to 3/4 in one step. Because you divided by the greatest common factor, the result is already in its lowest terms.
Can I find the GCF of more than two numbers?
Yes. The GCF Calculator takes up to 10 numbers at once. Behind the scenes it finds the GCF of the first two, then the GCF of that result and the next number, and so on, which gives the same answer as comparing them all together.
Where is the GCF used in real life?
Anywhere you need equal groups or a simpler ratio. A 1920 × 1080 screen has a GCF of 120, and 1920 ÷ 120 = 16 while 1080 ÷ 120 = 9, which is where the 16:9 aspect ratio comes from. It also helps split items into identical packs, scale recipes and cut tiles or boards without waste.
Which grades are these calculators suitable for?
Factors and the GCF usually appear from around grade 4 to 6 (class 5 to 7 in India), prime factorization in middle school, and the Euclidean algorithm in high school or a first computer science course. Because the calculator shows all three methods, one tool covers every stage.
Can I use a math calculator for homework?
Using it to check your answer and to see where your working went wrong is exactly what it is for. Copying the steps without following them will not help in a test, where you have to do it yourself, so try the problem first and then compare.
Which math calculators are coming next?
An LCM calculator, a prime factorization calculator, a fraction calculator, a percentage calculator and an algebra equation solver, all with step-by-step working. While you wait, Calcxi also has Finance and Business calculators, and you can request a math tool on the contact page.
Standard methods
Listing factors, prime factorization and the Euclidean algorithm, as taught in school maths.
Exact answers
Whole-number arithmetic with no rounding, so the result is exact every time.
Privacy
The numbers you enter are used to show the working and are not stored by Calcxi.
For learning
Built to help you check and understand your work. Follow your teacher's instructions on calculator use.
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