Number analysis
101
101 is a prime number — divisible only by 1 and itself.
101 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 101
- Digits
- 3
- Digit sum
- 2
- Reversed
- 101
- Palindrome
- Yes
1 + 0 + 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
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Twin prime
- Yes — paired with 103
- Nearest primes
- 97 ← → 103
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 6 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 101
The proper divisors — everything except n itself.
Its proper divisors fall short by 100.
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
1² + 10² = 101
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
- 25 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 2.
Peaks at 304 along the way.
Written other ways
- Binary
- 1100101
- Octal
- 145
- Hexadecimal
- 65
- Base 36
- 2T
- In words
- one hundred and one
- Scientific notation
- 1.01 × 10^2
Is 101 a prime number?
Yes. 101 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 101 their own way.
- Morse code
- · − − − − − − − − − · − − − −
- Devanagari
- १०१
- Tamil
- ௱௧
- Thai
- ๑๐๑
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.