Number analysis
105
105 is a composite odd number that factors as 3 × 5 × 7.
105 is a composite odd number that factors as 3 × 5 × 7.
The number itself
- Value
- 105
- Digits
- 3
- Digit sum
- 6
- Reversed
- 501
- Palindrome
- No
1 + 0 + 5
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 501.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3 × 5 × 7
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Nearest primes
- 103 ← → 107
Leaves remainder 1 on division by 2.
Composite — it factors as 3 × 5 × 7.
3 distinct prime factors, 3 with multiplicity.
No prime divides it twice.
(−1) to the power of 3 distinct prime factors.
A gap of 4 between them.
Divisors
- Aliquot sum
- 87
- Classification
- Deficient
1, 3, 5, 7, 15, 21, 35, 105
The proper divisors — everything except n itself.
Its proper divisors fall short by 18.
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
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
- Triangular number
- Yes — the 14th
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 38 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 6.
Peaks at 808 along the way.
Written other ways
- Binary
- 1101001
- Octal
- 151
- Hexadecimal
- 69
- Base 36
- 2X
- In words
- one hundred and five
- Scientific notation
- 1.05 × 10^2
Is 105 a prime number?
Composite — it factors as 3 × 5 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 105 their own way.
- Morse code
- · − − − − − − − − − · · · · ·
- Devanagari
- १०५
- Tamil
- ௱௫
- Thai
- ๑๐๕
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.