4968176400 has 360 divisors, whose sum is σ = 18997355520. Its totient is φ = 1192320000.

The previous prime is 4968176377. The next prime is 4968176413. The reversal of 4968176400 is 46718694.

It is a tau number, because it is divible by the number of its divisors (360).

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 71 ways as a sum of consecutive naturals, for example, 4315825 + ... + 4316975.

It is an arithmetic number, because the mean of its divisors is an integer number (52770432).

Almost surely, 2^4968176400 is an apocalyptic number.

4968176400 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 4968176400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9498677760).

4968176400 is an abundant number, since it is smaller than the sum of its proper divisors (14029179120).

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

4968176400 is a wasteful number, since it uses less digits than its factorization.

4968176400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1295 (or 1281 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 45.

The square root of 4968176400 is about 70485.2920828168. The cubic root of 4968176400 is about 1706.3403832490.

The spelling of 4968176400 in words is "four billion, nine hundred sixty-eight million, one hundred seventy-six thousand, four hundred".