Number analysis
167
167 is a prime number — divisible only by 1 and itself.
167 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 167
- Digits
- 3
- Digit sum
- 14
- Reversed
- 761
- Palindrome
- No
1 + 6 + 7
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 761.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Nearest primes
- 163 ← → 173
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 10 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 167
The proper divisors — everything except n itself.
Its proper divisors fall short by 166.
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
- No
- Sum of four squares
- Yes
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
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
- Yes
- Harshad number
- No
- Collatz trajectory
- 67 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 14.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 10100111
- Octal
- 247
- Hexadecimal
- A7
- Base 36
- 4N
- Roman numerals
- CLXVII
- In words
- one hundred and sixty-seven
- Scientific notation
- 1.67 × 10^2
Is 167 a prime number?
Yes. 167 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 167 their own way.
- Morse code
- · − − − − − · · · · − − · · ·
- Devanagari
- १६७
- Tamil
- ௱௬௰௭
- Thai
- ๑๖๗
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.