Elementary number theory is a branch of number theory that studies the divisibility of integers, indefinite equations and congruences by means of elementary mathematics. Its contents include division, factor, multiple, common factor, common multiple, greatest common factor, least common multiple, prime number and composite number. The number of prime numbers is infinite, basic arithmetic theorem, quadratic residue, perfect number, etc.

Number theory is also called "integer theory". It is a subject that studies the properties of numbers, especially the properties of integers. Its main branches are elementary number theory, algebraic number theory, carving degree approximation theory, number geometry, analytic number theory and so on.