7728400 has 45 divisors (see below), whose sum is σ = 18702021. Its totient is φ = 3069120.

The previous prime is 7728397. The next prime is 7728401. The reversal of 7728400 is 48277.

The square root of 7728400 is 2780.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 2782224 + 4946176 = 1668^2 + 2224^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (7728401) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 55531 + ... + 55669.

Almost surely, 2^7728400 is an apocalyptic number.

7728400 is the 2780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7728400

7728400 is an abundant number, since it is smaller than the sum of its proper divisors (10973621).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

7728400 is a wasteful number, since it uses less digits than its factorization.

7728400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 296 (or 146 counting only the distinct ones).

The product of its (nonzero) digits is 3136, while the sum is 28.

The cubic root of 7728400 is about 197.7105589671.

Multiplying 7728400 by its product of nonzero digits (3136), we get a square (24236262400 = 155680²).

It can be divided in two parts, 7728 and 400, that added together give a triangular number (8128 = T₁₂₇).

The spelling of 7728400 in words is "seven million, seven hundred twenty-eight thousand, four hundred".