FACTOR · VERIFY · UNDERSTAND
Factor Calculator
Enter one integer to see every factor, factor pair, prime power, divisor total, and number-theory profile — exactly, not approximately.
64-bitexact integer range
allpositive factors
localno account or server
FACTOR LAB
One number, fully factored
Signed integers are accepted. Zero is rejected because it has infinitely many non-zero integer divisors. Magnitude is limited to 264 − 1 so primality remains deterministic.
COMPOSITE · ABUNDANT2³ × 3² × 5
360 has 24 positive factors.
factor count τ(n)24
sum σ(n)1,170
proper-factor sum810
largest proper180
ALL FACTORS
24 positive factors
FACTOR PAIRS
12 multiplication pairs
prime/compositecomposite
perfect squareno
parityeven
distinct primes3
Euler φ(n)96
rad(n)30
Möbius μ(n)0
COMPARE TWO NUMBERS
Common factors without leaving the page
Omni-style two-number comparison, with both full factor sets still visible.
GCF428 common factors
Factors of 126
WHY THESE ARE THE FACTORS
Prime powers build every divisor
Count them
Sum them
Classify the number
DAILY 12
Train factor sense
0 / 0best —
FACTOR COUNT
Loading…
Type your answer.
FOCUSED PRACTICE
Generate another factor challenge
0 / 0streak 0
MIXED
Loading…
Type your answer.
Factors come in pairs
If d divides n, then n ÷ d is another factor. You only need to search to √n to discover every pair.
Prime powers count divisors
If n = pᵃqᵇ…, then τ(n) = (a+1)(b+1)… because each divisor chooses an exponent for each prime.
Perfect squares have an odd count
Only a square has one unpaired middle divisor: √n. That makes its positive divisor count odd.
Proper factors classify numbers
If their sum equals n the number is perfect; above n is abundant; below n is deficient.
Exactness, algorithm & scope
Exact BigInt arithmetic
Input parsing, prime factorization, divisor enumeration, τ(n), σ(n), Euler φ(n), radical, and common-factor comparison use integer arithmetic with no floating-point rounding.
Deterministic 64-bit prime testing
Primality uses a deterministic Miller–Rabin base set valid across the declared unsigned 64-bit range. Composite splitting uses Pollard–Rho/Brent with exact divisibility checks.
Signed-factor convention
The default factor list shows positive factors, matching standard school and calculator convention. Turn on signed factors to show ±d. Number-theory metrics still refer to the positive divisors of |n|.