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167 (number)

 ← 166 167 168 →
Cardinal one hundred sixty-seven
Ordinal 167th
(one hundred sixty-seventh)
Factorization prime
Prime 39th
Divisors 1, 167
Greek numeral ΡΞΖ´
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.

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In mathematics

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

167 is the only prime which can not be expressed as a sum of seven or fewer cubes. It is also the smallest number which requires six terms when expressed using the greedy algorithm as a sum of squares, 167 = 144 + 16 + 4 + 1 + 1 + 1,[2] although by Lagrange's four-square theorem its non-greedy expression as a sum of squares can be shorter, e.g. 167 = 121 + 36 + 1 + 1.

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 the smallest positive integer d such that the imaginary quadratic field Q(d) has class number = 11.[3]

167 is also: