7985174400 has 768 divisors, whose sum is σ = 34018060800. Its totient is φ = 1813985280.

The previous prime is 7985174377. The next prime is 7985174437. The reversal of 7985174400 is 44715897.

It is a happy number.

7985174400 is a `hidden beast` number, since 7 + 98 + 517 + 4 + 40 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 48988719 + ... + 48988881.

It is an arithmetic number, because the mean of its divisors is an integer number (44294350).

Almost surely, 2^7985174400 is an apocalyptic number.

7985174400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7985174400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17009030400).

7985174400 is an abundant number, since it is smaller than the sum of its proper divisors (26032886400).

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

7985174400 is an equidigital number, since it uses as much as digits as its factorization.

7985174400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 215 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 282240, while the sum is 45.

The square root of 7985174400 is about 89359.8030436504. The cubic root of 7985174400 is about 1998.7637693577.

The spelling of 7985174400 in words is "seven billion, nine hundred eighty-five million, one hundred seventy-four thousand, four hundred".