# 167 (number)

 ← 166 167 168 →
Cardinal one hundred sixty-seven
Ordinal 167th
(one hundred and sixty-seventh)
Factorization prime
Prime 39th
Divisors 1, 167
Roman numeral CLXVII
Binary 101001112
Ternary 200123
Quaternary 22134
Quinary 11325
Senary 4356
Octal 2478
Duodecimal 11B12
Vigesimal 8720
Base 36 4N36

167 (one hundred [and] sixty-seven) is the natural number following 166 and preceding 168.

## In mathematics

167 is a Chen prime, a Gaussian prime, a safe prime, and an Eisenstein prime with no imaginary part and a real part of the form $3n - 1$.

167 is the only prime which can't be expressed as a sum of seven or less cubes.

167 is a full reptend prime in base 10, since the decimal expansion of 1/167 repeats the following 166 digits: 0.00598802395209580838323353293413173652694610778443113772455089820359281437125748502994 0119760479041916167664670658682634730538922155688622754491017964071856287425149700...

167 is a highly cototient number, as it is the smallest number k with exactly 15 solutions to the equation x - φ(x) = k. It is also a strictly non-palindromic number.

167 is the smallest multi-digit prime such that the product of digits is equal to the number of digits times the sum of the digits, i. e., 1×6×7 = 3×(1+6+7)

167 is also: