Prime Divisor Calculator

Any whole number from 1 to 9,007,199,254,740,991.
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

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