# 171 (number)

171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.

 ← 170 171 172 →
Cardinalone hundred seventy-one
Ordinal171st
(one hundred seventy-first)
Factorization32 × 19
Divisors1, 3, 9, 19, 57, 171
Greek numeralΡΟΑ´
Roman numeralCLXXI
Binary101010112
Ternary201003
Senary4436
Octal2538
Duodecimal12312

## In mathematics

171 is a triangular number and a Jacobsthal number.

There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices.

The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon.

There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.

Within moonshine theory of sporadic groups, the friendly giant $\mathbb {M}$  is defined as having cyclic groups$m$  ⟩ that are linked with the function,

$f_{m}(\tau )=q^{-1}+a_{1}q+a_{2}q^{2}+...,{\text{ }}a_{k}$ $\mathbb {Z} ,{\text{ }}q=e^{2\pi i\tau },{\text{ }}\tau >0;$  where $q$  is the character of $\mathbb {M}$  at $m$ .

This generates 171 moonshine groups within $\mathbb {M}$  associated with $f_{m}$  that are principal moduli for different genus zero congruence groups commensurable with the projective linear group $\operatorname {PSL_{2}} (\mathbb {Z} )$ .

It is the number of 3-digit Duck Numbers, i.e., Numbers with at least one digit zero, in Decimal Base.