4153766400 has 960 divisors, whose sum is σ = 18632021760. Its totient is φ = 884736000.

The previous prime is 4153766389. The next prime is 4153766531. The reversal of 4153766400 is 46673514.

It is a happy number.

4153766400 is a `hidden beast` number, since 4 + 1 + 5 + 3 + 7 + 6 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 41126350 + ... + 41126450.

It is an arithmetic number, because the mean of its divisors is an integer number (19408356).

Almost surely, 2^4153766400 is an apocalyptic number.

4153766400 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 4153766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9316010880).

4153766400 is an abundant number, since it is smaller than the sum of its proper divisors (14478255360).

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

4153766400 is a wasteful number, since it uses less digits than its factorization.

4153766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 162 (or 135 counting only the distinct ones).

The product of its (nonzero) digits is 60480, while the sum is 36.

The square root of 4153766400 is about 64449.7199373279. The cubic root of 4153766400 is about 1607.4865814656.

The spelling of 4153766400 in words is "four billion, one hundred fifty-three million, seven hundred sixty-six thousand, four hundred".