4768826400 has 1008 divisors, whose sum is σ = 20441207304. Its totient is φ = 1074954240.

The previous prime is 4768826393. The next prime is 4768826431. The reversal of 4768826400 is 46288674.

It can be written as a sum of positive squares in 12 ways, for example, as 831514896 + 3937311504 = 28836^2 + 62748^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 128887182 + ... + 128887218.

Almost surely, 2^4768826400 is an apocalyptic number.

4768826400 is a gapful number since it is divisible by the number (40) 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 4768826400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10220603652).

4768826400 is an abundant number, since it is smaller than the sum of its proper divisors (15672380904).

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

4768826400 is a wasteful number, since it uses less digits than its factorization.

4768826400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 105 (or 77 counting only the distinct ones).

The product of its (nonzero) digits is 516096, while the sum is 45.

The square root of 4768826400 is about 69056.6897555914. The cubic root of 4768826400 is about 1683.2056141594.

It can be divided in two parts, 47688 and 26400, that added together give a cube (74088 = 42³).

The spelling of 4768826400 in words is "four billion, seven hundred sixty-eight million, eight hundred twenty-six thousand, four hundred".