Factor Calculator
Find all factors and factor pairs of a number with prime, composite, and perfect number detection.
Number details
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Number
Integer ?
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Second integer ?
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Try an example
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Factor list separator
Factor pairs layout
All factors
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Factor pairs
—| Factor | × | Factor | Product |
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Step-by-step factorization
Trial division by ascending primes.GCD & LCM
—GCD
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LCM
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Coprime?
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Formula
τ(n)
=
(a1+1)
·
(a2+1)
·
…
·
(ak+1)
- n
- The integer being analyzed (n ≥ 1)
- piai
- Prime pi raised to its multiplicity ai in n's factorization
- τ(n)
- Number of positive divisors — product of (ai+1)
- σ(n)
- Sum of divisors — ∏ (piai+1−1) / (pi−1)
- s(n)
- Aliquot sum — σ(n) − n. Classifies n as deficient, perfect, or abundant.
WORKED EXAMPLE — YOUR NUMBER
- Start with —
- Factor into primes: —
- Divisor count τ(n) = —
- Divisor sum σ(n) = —
- Aliquot sum s(n) = — — —
A positive integer n has exactly τ(n) factors, laid out as pairs (d, n/d) that meet at √n. When n is a perfect square, one pair collapses (√n × √n), giving an odd factor count — perfect squares are the only integers with an odd number of divisors.