7846416400 has 135 divisors (see below), whose sum is σ = 19488800349. Its totient is φ = 3035813760.

The previous prime is 7846416299. The next prime is 7846416439. The reversal of 7846416400 is 46146487.

The square root of 7846416400 is 88580.

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., 2824709904 + 5021706496 = 53148^2 + 70864^2 .

It is a Smith number, since the sum of its digits (40) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 76178749 + ... + 76178851.

Almost surely, 2^7846416400 is an apocalyptic number.

7846416400 is the 88580-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7846416400

7846416400 is an abundant number, since it is smaller than the sum of its proper divisors (11642383949).

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

7846416400 is a wasteful number, since it uses less digits than its factorization.

7846416400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 310 (or 153 counting only the distinct ones).

The product of its (nonzero) digits is 129024, while the sum is 40.

The cubic root of 7846416400 is about 1987.1185792858.

It can be divided in two parts, 78464 and 16400, that added together give a square (94864 = 308²).

The spelling of 7846416400 in words is "seven billion, eight hundred forty-six million, four hundred sixteen thousand, four hundred".