Number analysis
108
A sacred count in Hinduism and Buddhism, and the number of beads on a mala.
A sacred count in Hinduism and Buddhism, and the number of beads on a mala.
The number itself
- Value
- 108
- Digits
- 3
- Digit sum
- 9
- Reversed
- 801
- Palindrome
- No
1 + 0 + 8
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 801.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^2 × 3^3
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 107 ← → 109
Divisible by 2.
Composite — it factors as 2^2 × 3^3.
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
- 172
- Classification
- Abundant
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The proper divisors — everything except n itself.
Its proper divisors overshoot by 64.
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
- Goldbach pair
- 5 + 103
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.
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
- 113 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 108 ÷ 9 = 12.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 1101100
- Octal
- 154
- Hexadecimal
- 6C
- Base 36
- 30
- Roman numerals
- CVIII
- In words
- one hundred and eight
- Scientific notation
- 1.08 × 10^2
Is 108 a prime number?
Composite — it factors as 2^2 × 3^3.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 108 their own way.
- Morse code
- · − − − − − − − − − − − − · ·
- Devanagari
- १०८
- Tamil
- ௱௮
- Thai
- ๑๐๘
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.