174 (number)

174 (one hundred [and] seventy-four) is the natural number following 173 and preceding 175.

← 173 174 175 →
← 170 171 172 173 174 175 176 177 178 179 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred seventy-four
Ordinal	174th (one hundred seventy-fourth)
Factorization	2 × 3 × 29
Divisors	1, 2, 3, 6, 29, 58, 87, 174
Greek numeral	ΡΟΔ´
Roman numeral	CLXXIV, clxxiv
Binary	101011102
Ternary	201103
Senary	4506
Octal	2568
Duodecimal	12612
Hexadecimal	AE16

In mathematics

There are 174 7-crossing semi-meanders, ways of arranging a semi-infinite curve in the plane so that it crosses a straight line seven times.^[1] There are 174 invertible ${\displaystyle 3\times 3}$ (0,1)-matrices.^[2][3] There are also 174 combinatorially distinct ways of subdividing a topological cuboid into a mesh of tetrahedra, without adding extra vertices, although not all can be represented geometrically by flat-sided polyhedra.^[4]

The Mordell curve ${\displaystyle y^{2}=x^{3}-174}$ has rank three, and 174 is the smallest positive integer for which ${\displaystyle y^{2}=x^{3}-k}$ has this rank. The corresponding number for curves ${\displaystyle y^{2}=x^{3}+k}$ is 113.^[5][6]

See also

• All pages with titles containing 174