Number analysis
72
72 is a composite even number that factors as 2^3 × 3^2.
72 is a composite even number that factors as 2^3 × 3^2.
The number itself
- Value
- 72
- Digits
- 2
- Digit sum
- 9
- Reversed
- 27
- Palindrome
- No
7 + 2
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 27.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^3 × 3^2
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 71 ← → 73
Divisible by 2.
Composite — it factors as 2^3 × 3^2.
2 distinct prime factors, 5 with multiplicity.
At least one prime appears squared.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 2 between them.
Divisors
- Aliquot sum
- 123
- Classification
- Abundant
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The proper divisors — everything except n itself.
Its proper divisors overshoot by 51.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- Yes
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Sum of two cubes
- 2³ + 4³
- Goldbach pair
- 5 + 67
6² + 6² = 72
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 22 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 72 ÷ 9 = 8.
Peaks at 72 along the way.
Written other ways
- Binary
- 1001000
- Octal
- 110
- Hexadecimal
- 48
- Base 36
- 20
- Roman numerals
- LXXII
- In words
- seventy-two
- Scientific notation
- 7.2 × 10^1
Is 72 a prime number?
Composite — it factors as 2^3 × 3^2.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 72 their own way.
- Greek (alphabetic)
- ΟΒʹ
- Babylonian cuneiform
- 𒐕𒌋𒐖
- Tamil
- ௭௰௨
References
Further reading: Wikipedia · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.