GCF and LCM of 72
Every pair this site works through that contains 72. 30 of them share a factor with it; 0 share nothing, which is its own kind of answer.
Shares a factor with 72
with 2: 2with 3: 3with 4: 4with 6: 6with 8: 8with 9: 9with 10: 2with 12: 12with 14: 2with 15: 3with 16: 8with 18: 18with 20: 4with 24: 24with 27: 9with 30: 6with 32: 8with 36: 36with 40: 8with 45: 9with 48: 24with 50: 2with 60: 12with 64: 8with 75: 3with 80: 8with 90: 18with 96: 24with 100: 4with 120: 24
What 72 is made of
Every common factor 72 can share with anything comes from this list, which is why the pairs below look the way they do. 72 = 2³ × 3², and that factorisation is unique — the fundamental theorem of arithmetic guarantees no other set of primes multiplies to it.
- Divisors (12)
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- As factor pairs
- 1×72, 2×36, 3×24, 4×18, 6×12, 8×9
- Prime factorisation
- 2³ × 3²
- Divisors excluding itself add to
- 123 — abundant
Divisors come in pairs that multiply to 72, which is why there is an even number of them unless the number is a perfect square. The greatest common factor of 72 and any other number is the largest entry two lists like this one share.