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Arithmetic and number theory calculators

Calculators for the four operations, percentages, ratios, simple averages and the properties of whole numbers. They show column and long-division working for students checking homework, and give exact answers for numbers of any size.

Which calculator do I need?

You have or wantUse
Long division with the remainder and the repeating decimalDivision calculator
What percent one number is of another, or a percentage increasePercentage calculator
Share an amount in the ratio 2 : 3, or solve a : b = c : xRatio and proportion calculator
An average where some values count more than othersWeighted average calculator
Whether a number is prime, or the next prime after itPrime number calculator
A factor tree and the full list of divisorsPrime factorization calculator
The highest common factor or lowest common multipleGCD and LCM calculator
A number in binary, hex or another baseNumber system converter

The four operations

Exact sums, differences, products and quotients with the written method shown.

Percentages, ratios and averages

Comparing amounts: as a percentage, as a ratio, or as the average of a list.

Primes, factors and divisibility

Breaking whole numbers into their building blocks and finding what they share.

Number theory and number bases

Remainders, special functions of integers, and writing numbers in other bases.

How these calculators fit together

The first four pages do one operation each and show the written method taught in school: carries for addition, borrows for subtraction, partial products for multiplication and the bring-down steps of long division. Use them to check working, not only the answer.

Percentages and ratios are two ways of comparing amounts. The percentage calculator compares against 100; the ratio calculator compares parts with each other. The average, weighted average and grade average calculators summarise a list with one number. For the median, mode and range, see the averages hub in statistics.

The prime and factor pages all rest on the same fact: every whole number above 1 is a product of primes in exactly one way. Once you have the prime factorization, the GCD, LCM and divisor count follow.

Worked comparison: GCD and LCM of 12 and 18

NumberPrime factors
122² × 3
182 × 3²
GCD (lowest powers)2 × 3 = 6
LCM (highest powers)2² × 3² = 36

As a check, GCD × LCM = 6 × 36 = 216 = 12 × 18, which holds for any two positive whole numbers. The GCD and LCM calculator also runs the Euclidean algorithm, which is quicker for large numbers: 18 = 1 × 12 + 6, then 12 = 2 × 6 + 0, so the GCD is 6.

Common mix-ups

  • Percentage change is not symmetric. Going from 40 to 50 is a 25% rise, but going back from 50 to 40 is a 20% fall, because the base changes.
  • Percent versus percentage points. A rate moving from 4% to 5% has risen by one percentage point, which is a 25% increase.
  • Remainder versus mod of a negative number. Many programming languages give −7 % 3 = −1, while mathematics gives −7 mod 3 = 2. The modular arithmetic calculator uses the mathematical convention.

Guides to read alongside

Common questions

What is the difference between the GCD, GCF and HCF?
They are the same thing under different names: greatest common divisor, greatest common factor and highest common factor. Each is the largest whole number that divides all of the given numbers without a remainder.
Is 1 a prime number?
No. A prime has exactly two positive divisors, 1 and itself, and 1 has only one. Leaving 1 out is what keeps prime factorization unique; otherwise 6 could be written as 2 × 3, 1 × 2 × 3, 1 × 1 × 2 × 3 and so on.
How do I find a number before a percentage increase?
Divide by one plus the rate, not subtract the percentage. A price of 120 after a 20% rise was 120 ÷ 1.2 = 100 before it; taking 20% off 120 gives 96, which is wrong. The reverse-percentage mode of the percentage calculator does this for you.

Written and reviewed by our editorial team. Last updated . Method and sources: how these numbers are computed.