Number analysis
144
The only Fibonacci number besides 0 and 1 that is also a perfect square. A gross.
The only Fibonacci number besides 0 and 1 that is also a perfect square. A gross.
The number itself
- Value
- 144
- Digits
- 3
- Digit sum
- 9
- Reversed
- 441
- Palindrome
- No
1 + 4 + 4
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 441.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^4 × 3^2
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 139 ← → 149
Divisible by 2.
Composite — it factors as 2^4 × 3^2.
2 distinct prime factors, 6 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 10 between them.
Divisors
- Aliquot sum
- 259
- Classification
- Abundant
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The proper divisors — everything except n itself.
Its proper divisors overshoot by 115.
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
- Goldbach pair
- 5 + 139
0² + 12² = 144
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
- Square number
- Yes — the 12th
- Fibonacci number
- Yes — index 12
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 23 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 144 ÷ 9 = 16.
Peaks at 144 along the way.
Written other ways
- Binary
- 10010000
- Octal
- 220
- Hexadecimal
- 90
- Base 36
- 40
- Roman numerals
- CXLIV
- In words
- one hundred and forty-four
- Scientific notation
- 1.44 × 10^2
Is 144 a prime number?
Composite — it factors as 2^4 × 3^2.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 144 their own way.
- Morse code
- · − − − − · · · · − · · · · −
- Devanagari
- १४४
- Tamil
- ௱௪௰௪
- Thai
- ๑๔๔
References
Further reading: Wikipedia · MathWorld · 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.