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Prime factorization

Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime.

Visit numtheory.openverbs.com

Host	numtheory.openverbs.com
Price	$0.004 per call
Network	Base
Paid endpoints listed	6
Calls, last 30 days*	8
Most unique payers on one endpoint (30 days)*	2
Last paid call*	2026-10-08
Tags	prime factorization, factor integer, integer factors api, prime factors lookup, divisor count, greatest common divisor, compute gcd, gcd api

* From the public x402 Bazaar index (snapshot 2026-10-18T04:07Z); reported by the facilitator, not measured by us.

Endpoints

URL	Method	Price
`https://numtheory.openverbs.com/v1/factorize` Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with…	POST	$0.004
`https://numtheory.openverbs.com/v1/gcd` Greatest common divisor of two or more non-negative integers (arbitrary precision).	POST	$0.004
`https://numtheory.openverbs.com/v1/totient` Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed…	POST	$0.004
`https://numtheory.openverbs.com/v1/modpow` Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive.	POST	$0.004
`https://numtheory.openverbs.com/v1/lcm` Least common multiple of two or more positive integers (arbitrary precision).	POST	$0.004
`https://numtheory.openverbs.com/v1/is-prime` Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer.…	POST	$0.004

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