7826738400 has 864 divisors, whose sum is σ = 32644160640. Its totient is φ = 1813985280.

The previous prime is 7826738363. The next prime is 7826738401. The reversal of 7826738400 is 48376287.

It is a happy number.

7826738400 is a `hidden beast` number, since 7 + 8 + 267 + 384 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-2 number, since 2×7826738400² (a number of 21 digits) contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7826738401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 48016719 + ... + 48016881.

Almost surely, 2^7826738400 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7826738400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16322080320).

7826738400 is an abundant number, since it is smaller than the sum of its proper divisors (24817422240).

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

7826738400 is a wasteful number, since it uses less digits than its factorization.

7826738400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 230 (or 205 counting only the distinct ones).

The product of its (nonzero) digits is 451584, while the sum is 45.

The square root of 7826738400 is about 88468.8555368498. The cubic root of 7826738400 is about 1985.4560261156.

The spelling of 7826738400 in words is "seven billion, eight hundred twenty-six million, seven hundred thirty-eight thousand, four hundred".