Big Number Calculator: Factorials, Powers, GCD

The Big Number Calculator performs exact integer arithmetic on values that ordinary floating-point calculators cannot hold. Addition, subtraction, multiplication, division, modulo, powers, integer roots, factorials, GCD, LCM and trial prime factorisation all return full digit strings rather than scientific approximations. Digit count and optional precision controls accompany every result so the size of the answer is visible at a glance.

All calculation runs in your browser. Nothing you enter is sent to a server.

Calculate with numbers beyond standard precision

Arbitrary-precision integers grow as large as memory allows. Enter operands as decimal digit strings, or with 0x / 0b prefixes when hex or binary input is convenient, and choose an operation. The primary output is the exact result; a secondary field reports how many digits it contains.

Standard calculators stop being exact long before cryptography or combinatorics care. Factorials, large powers and products of many terms overflow IEEE floats into infinity or round away low digits. This tool keeps every digit for integer results, which is the point of the page.

Understand where standard calculators lose accuracy

IEEE-754 double precision carries about 15 to 17 significant decimal digits. Integers above 2⁵³ (9,007,199,254,740,992) cannot all be represented exactly in a double; past that point, odd integers are rounded to nearby even ones. Pocket calculators and spreadsheet cells that use doubles therefore lie quietly on large whole numbers.

2^53 = 9007199254740992   last consecutive integer a double holds exactly
2^53 + 1                  cannot be distinguished from 2^53 in a double

Floating-point multiplication and division also introduce rounding error on fractional results. The Big Number Calculator avoids that class of error for integer operations by using big-integer arithmetic. Non-integer roots and divisions still need a precision setting, because those results are not finite digit strings by nature.

Run arithmetic on very large integers

Addition, subtraction, multiplication, division and modulo accept operands of hundreds or thousands of digits. Division returns an integer quotient; modulo returns the remainder with the usual sign conventions for the engine. Multiplying two 100-digit numbers produces up to a 200-digit product without scientific notation hiding the middle.

Borrowing and carrying follow the same rules as hand arithmetic, extended across digit arrays. Performance stays interactive for sizes common in homework and programming contests; pathological inputs with tens of thousands of digits may pause the tab while the browser works. Cancel and retry with a smaller case if the page becomes unresponsive.

Calculate powers, roots and factorials

Powers compute base^exponent for non-negative integer exponents with an exact integer result. Integer square roots return the floor of the true root and can show the remainder. Factorial n! multiplies every integer from 1 through n and returns the full digit string, which for 100! is 158 digits long and far past what a double can store exactly.

100! has 158 digits. The leading digits are 9332621544… and the full string is too long for casual handwriting, which is why the calculator exists. Digit count alone answers many contest checks: if a problem asks whether 100! fits in a 256-bit register, 158 decimal digits is already more than enough to decide (256 bits hold at most 78 decimal digits).

n	n! (trailing form)	Digits
10	3,628,800	7
20	2,432,902,008,176,640,000	19
50	(long)	65
100	(long)	158

Negative factorials are undefined for integers. Very large n will eventually exhaust browser memory; the tool reports failure rather than returning a truncated value.

Find the greatest common divisor and lowest common multiple

GCD uses the Euclidean algorithm: replace the larger number by the remainder of division until the remainder is zero. The last non-zero remainder is the GCD. LCM follows from LCM(a, b) = |a × b| / GCD(a, b) with big-integer multiplication so the product does not overflow.

Coprime integers have GCD 1. Reducing a fraction or an aspect ratio is GCD division on both terms; the Aspect Ratio Calculator owns that UI, while this page exposes the raw GCD and LCM operations for arbitrary integers. Entering 1920 and 1080 yields GCD 120, which is the same factor that reduces a Full HD frame to 16:9.

Find prime factors of a large number

Trial division peels off small prime factors, then continues upward against the remaining cofactor until that cofactor is prime or the search limit is hit. Semiprimes built from two large primes are the hard case: trial division will not finish interactively in a browser, and the page states that limit rather than hanging silently.

Input	Factors
12	2² × 3
97	97 (prime)
1,001	7 × 11 × 13

The calculator states limits honestly. Numbers with small factors factor quickly. Numbers built like RSA moduli will not finish in interactive time, and that is expected: cryptography relies on that difficulty. For teaching and contest problems with moderate composites, the factorisation view is enough.

Set the precision for non-exact results

Square roots of non-perfect squares and divisions that do not land on integers need a precision setting: a number of significant digits to compute before rounding. Scientific notation is available for very large or very small magnitudes when the full digit string is unwieldy.

Integer-only operations ignore the precision control because the exact answer is finite. Mixing modes is a common mistake: setting precision to 10 does not truncate 100!; factorial still returns all 158 digits. Precision applies to approximate operations only.

Use big numbers in practice

Cryptography talks about key sizes in bits: a 2048-bit RSA modulus is a roughly 617-digit decimal integer. Combinatorics produces factorials and binomial coefficients that outgrow 64-bit registers immediately. Competitive programming problems often ask for answers modulo a prime, which still needs big intermediate products before reduction.

When a language offers a built-in big-integer type (Python int, Java BigInteger, JavaScript BigInt), this calculator is a scratch pad for checking those programs. When a language is stuck on doubles, the calculator is the reference for what the exact value should have been.

Frequently asked questions

Summary

The Big Number Calculator keeps exact integer results where doubles lose digits past roughly 15 significant figures and past 2⁵³. Arithmetic, powers, factorials, GCD, LCM and trial factorisation run locally, with 100! reported as a 158-digit integer. Precision controls apply to non-integer roots and divisions only. Cryptography-scale factorisation is acknowledged as out of scope for interactive trial division.