FreeTools Labs Glossary
Numbers, bases and divisors
Learn how numbers are represented in different bases and how place values, divisors, factors and prime numbers describe their structure.
Relevant tool
Number & Numeral System Calculator
Prime numbers, factors, GCD, LCM, numeral systems and Roman numerals.
Open Number & Numeral System Calculator →Numbers can be written in different positional systems. Divisibility, factors and primes reveal more about their structure.
Base and place value
In decimal, each position represents a power of ten. Binary uses base two, octal base eight and hexadecimal base sixteen.
A digit's value therefore depends on its position and base. Bases above ten use letters for additional digits.
Convert between bases
A numeral is built from digits multiplied by powers of its base. To convert an integer to another base, repeatedly divide by the target base.
Place value
(d_n … d_0)_b = Σ d_i × b^iPrimes, factors and divisors
A prime has exactly two positive divisors: one and itself. Prime factorisation writes a positive integer as a product of primes.
Greatest common divisor and least common multiple help with simplification, common denominators and repeating cycles.
Practical uses
Binary and hexadecimal are common in computing and electronics because they relate well to bits. Roman numerals are historical notation, not an ordinary positional system.
Changing the base changes a number's representation, not its mathematical value.
Use valid inputs
A digit must be smaller than the base: 8 is invalid in octal. Factor and prime operations in the tool apply to integers.
Very large values can meet practical software limits even though number theory goes further.
How our number-system calculator works
Our calculator converts integers between bases 2 and 36 and provides prime checks, divisors, factors, prime factorisation, GCD and LCM. Roman numerals are also supported.
Inputs are validated against the selected base and applicable integer range. The tool calculates defined properties; it is not a complete number-theory system.