Number analysis
121
121 is a composite odd number that factors as 11^2.
121 is a composite odd number that factors as 11^2.
The number itself
- Value
- 121
- Digits
- 3
- Digit sum
- 4
- Reversed
- 121
- Palindrome
- Yes
1 + 2 + 1
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 11^2
- Squarefree
- No
- Semiprime
- Yes
- Prime power
- 11^2
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 113 ← → 127
Leaves remainder 1 on division by 2.
Composite — it factors as 11^2.
1 distinct prime factor, 2 with multiplicity.
At least one prime appears squared.
A product of exactly two primes, counted with multiplicity.
A single prime raised to a power.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 14 between them.
Divisors
- Aliquot sum
- 12
- Classification
- Deficient
1, 11, 121
The proper divisors — everything except n itself.
Its proper divisors fall short by 109.
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
0² + 11² = 121
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Square number
- Yes — the 11th
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 95 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 4.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 1111001
- Octal
- 171
- Hexadecimal
- 79
- Base 36
- 3D
- Roman numerals
- CXXI
- In words
- one hundred and twenty-one
- Scientific notation
- 1.21 × 10^2
Is 121 a prime number?
Composite — it factors as 11^2.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 121 their own way.
- Morse code
- · − − − − · · − − − · − − − −
- Devanagari
- १२१
- Tamil
- ௱௨௰௧
- Thai
- ๑๒๑
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.