744 (number)

← 743 744 745 →
List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	seven hundred forty-four
Ordinal	744th; (seven hundred forty-fourth)
Factorization	23 × 3 × 31
Divisors	1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744
Greek numeral	ΨΜΔ´
Roman numeral	DCCXLIV, dccxliv
Binary	10111010002
Ternary	10001203
Senary	32406
Octal	13508
Duodecimal	52012
Hexadecimal	2E816

744 (seven hundred [and] forty four) is the natural number following 743 and preceding 745.

In mathematics

The $j$ -invariant, an important function in the study of modular forms and Monstrous moonshine, can be written as a Fourier series in which the constant term is 744:^[4] $j(\tau )=q^{-1}+744+196\,884q+21\,493\,760q^{2}+864\,299\,970q^{3}+\cdots ,$ where $q=e^{2\pi i\tau }$ . One consequence of this is that 744 appears in expressions for Ramanujan's constant and other almost integers.

Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory (analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, p-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers p-adic numbers (p-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Irrationality measure Simple continued fractions
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