Factor Calculator

Any whole number from 1 to 9,007,199,254,740,991.
Every figure below is computed either way; this only chooses which one is the answer.
Prime factorization
2^3 x 3^2 x 5
Prime Factorization Calculator
Written out in full
2 x 2 x 2 x 3 x 3 x 5
Number of distinct primes
3
Prime factors counted with multiplicity
6
Is prime
No
Smallest prime factor
2
Largest prime factor
5
Number of divisors
24
Sum of divisors
1,170
Sum of proper divisors
810
Euler's totient
96
Radical (product of distinct primes)
30
Perfect, abundant or deficient
Abundant
Square-free
No
Worked out from NIST Digital Library of Mathematical Functions, ยง27.2-27.3 (fundamental theorem of arithmetic; divisor and totient functions) and 2 other sources.

How this is worked out

9 steps
  1. 360 / 2 = 180
  2. 180 / 2 = 90
  3. 90 / 2 = 45
  4. 45 / 3 = 15
  5. 15 / 3 = 5
  6. 5 / 5 = 1
  7. Nothing left to divide, so 360 = 2^3 x 3^2 x 5.
  8. Number of divisors = product of (exponent + 1) = (3+1) x (2+1) x (1+1) = 24.
  9. Sum of divisors = product of (p^(e+1)-1)/(p-1) = 1170; subtracting 360 leaves 810 for the proper divisors.
Distinct prime factorstable
2, 3, 5
Exponent of each primetable
3, 2, 1
All divisorstable
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Results are general information, not financial, tax, legal, medical or engineering advice.