Number of Divisors Calculator

About this calculator

The divisor function d(n) counts how many positive integers evenly divide a whole number n. The efficient way to compute it, and the method this calculator uses, is trial division up to the square root of n: every divisor found below the square root pairs with a corresponding divisor above it, so checking only up to √n and counting both members of each pair covers every divisor without brute-forcing the full range up to n.

Number theory connects this directly to prime factorization: if n factors as p1^a1 × p2^a2 × ... × pk^ak, then d(n) equals (a1+1) × (a2+1) × ... × (ak+1), which is why highly composite numbers like 12 or 60 have disproportionately many divisors relative to their size. Students studying number theory, and programmers working on divisor-related problems in competitive programming, use this count as a basic building block.

Enter any whole number and this calculator returns its total number of positive divisors along with the underlying factor logic.