Number analysis
153
The smallest non-trivial Armstrong number: 1³ + 5³ + 3³ = 153.
The smallest non-trivial Armstrong number: 1³ + 5³ + 3³ = 153.
The number itself
- Value
- 153
- Digits
- 3
- Digit sum
- 9
- Reversed
- 351
- Palindrome
- No
1 + 5 + 3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 351.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3^2 × 17
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 151 ← → 157
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2 × 17.
2 distinct prime factors, 3 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 6 between them.
Divisors
- Aliquot sum
- 81
- Classification
- Deficient
1, 3, 9, 17, 51, 153
The proper divisors — everything except n itself.
Its proper divisors fall short by 72.
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
3² + 12² = 153
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Triangular number
- Yes — the 17th
- Hexagonal number
- Yes — the 9th
Digit curiosities
- Happy number
- No
- Armstrong number
- Yes
- Harshad number
- Yes
- Collatz trajectory
- 36 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
1^3 + 5^3 + 3^3 = 153
Divisible by its digit sum 9 — 153 ÷ 9 = 17.
Peaks at 520 along the way.
Written other ways
- Binary
- 10011001
- Octal
- 231
- Hexadecimal
- 99
- Base 36
- 49
- Roman numerals
- CLIII
- In words
- one hundred and fifty-three
- Scientific notation
- 1.53 × 10^2
Is 153 a prime number?
Composite — it factors as 3^2 × 17.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 153 their own way.
- Morse code
- · − − − − · · · · · · · · − −
- Devanagari
- १५३
- Tamil
- ௱௫௰௩
- Thai
- ๑๕๓
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.