Number analysis
189
189 is a composite odd number that factors as 3^3 × 7.
189 is a composite odd number that factors as 3^3 × 7.
The number itself
- Value
- 189
- Digits
- 3
- Digit sum
- 18
- Reversed
- 981
- Palindrome
- No
1 + 8 + 9
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 981.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3^3 × 7
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 181 ← → 191
Leaves remainder 1 on division by 2.
Composite — it factors as 3^3 × 7.
2 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 10 between them.
Divisors
- Aliquot sum
- 131
- Classification
- Deficient
1, 3, 7, 9, 21, 27, 63, 189
The proper divisors — everything except n itself.
Its proper divisors fall short by 58.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Sum of two cubes
- 4³ + 5³
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
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
- No
- Collatz trajectory
- 106 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 18.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 10111101
- Octal
- 275
- Hexadecimal
- BD
- Base 36
- 59
- Roman numerals
- CLXXXIX
- In words
- one hundred and eighty-nine
- Scientific notation
- 1.89 × 10^2
Is 189 a prime number?
Composite — it factors as 3^3 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 189 their own way.
- Morse code
- · − − − − − − − · · − − − − ·
- Devanagari
- १८९
- Tamil
- ௱௮௰௯
- Thai
- ๑๘๙
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.