Math Calculators
Solve fractions, percentages, GCF, LCM, rounding and square-root problems with 8 free step-by-step calculators. Each one shows the method — like the Euclidean algorithm for GCF — with worked examples, so you learn the technique as well as the answer.
What can you solve with these math tools?
These 8 calculators handle the arithmetic that comes up most in school and everyday life: fractions (adding, simplifying, finding common denominators), number theory (greatest common factor, least common multiple), percentages, rounding to any place value, and square roots. Every tool shows the method step by step — the goal is to help you learn the technique, not just get the answer.
How are GCF, LCM and LCD related?
They are three views of the same structure. The GCF (greatest common factor) is the largest number dividing two numbers; the LCM (least common multiple) is the smallest number both divide into; and the LCD (least common denominator) is simply the LCM of two denominators. They connect through the identity GCF(a, b) × LCM(a, b) = a × b — for 12 and 18: GCF 6 × LCM 36 = 216 = 12 × 18.
Why do percentages trip so many people up?
Because "percent of" and "percent change" are different operations. 20% of 150 is 30, but increasing 150 by 20% gives 180, and a number that grows from 150 to 180 has increased by 20% while 180 reduced by 20% gives 144, not 150 — percentage changes are not symmetric. The Percentage Calculator handles all these variants explicitly so the right formula is always applied.
Frequently asked questions
The fastest method is the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until the remainder is 0 — the last non-zero value is the GCF. For 48 and 18: 48 ÷ 18 leaves 12, 18 ÷ 12 leaves 6, 12 ÷ 6 leaves 0, so the GCF is 6.
Multiply the number by the percentage divided by 100. So 15% of 240 is 240 × 0.15 = 36. To go the other way — what percent 36 is of 240 — divide and multiply by 100: 36 ÷ 240 × 100 = 15%.
Divide the numerator and denominator by their greatest common factor. For 24/36, the GCF is 12, so 24/36 simplifies to 2/3. The Fraction Simplifier finds the GCF automatically and shows the division.
No — square roots of perfect squares (1, 4, 9, 16, …) are whole numbers. But the square root of any non-perfect-square integer is irrational: √2 ≈ 1.41421356 was proven irrational by the ancient Greeks, and the same argument applies to √3, √5 and so on.