How to Calculate Number Theory
What is Number Theory?
Number theory is the branch of pure mathematics studying integers and their properties: prime numbers, divisibility, GCD, LCM, modular arithmetic, and Diophantine equations.
Formula
- LCM
- a×b / GCD(a — a×b / GCD(a
- GCD
- GCD value — Variable used in the calculation
Step-by-Step Guide
- 1Prime: divisible only by 1 and itself; test by trial division up to √n
- 2GCD: Euclidean algorithm — repeatedly apply modulo
- 3LCM(a,b) = a×b / GCD(a,b)
- 4Modular arithmetic: a ≡ b (mod n) if n divides (a−b)
Worked Examples
Frequently Asked Questions
What is Number Theory?
Number theory is the branch of pure mathematics studying integers and their properties: prime numbers, divisibility, GCD, LCM, modular arithmetic, and Diophantine equations. Use this calculator for accurate, instant results.
How accurate is the Number Theory calculator?
The calculator uses the standard published formula for number theory. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Number Theory calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Number Theory calculator use?
The core formula is: LCM(a,b) = a×b / GCD(a,b). Each step in the calculation is shown so you can verify the result manually.