4117142400 has 384 divisors, whose sum is σ = 15626856960. Its totient is φ = 933273600.

The previous prime is 4117142389. The next prime is 4117142413. The reversal of 4117142400 is 42417114.

4117142400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 13238245 + ... + 13238555.

It is an arithmetic number, because the mean of its divisors is an integer number (40694940).

Almost surely, 2^4117142400 is an apocalyptic number.

4117142400 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 4117142400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7813428480).

4117142400 is an abundant number, since it is smaller than the sum of its proper divisors (11509714560).

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

4117142400 is a wasteful number, since it uses less digits than its factorization.

4117142400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 542 (or 525 counting only the distinct ones).

The product of its (nonzero) digits is 896, while the sum is 24.

The square root of 4117142400 is about 64164.9624016098. The cubic root of 4117142400 is about 1602.7481936090.

Adding to 4117142400 its reverse (42417114), we get a palindrome (4159559514).

The spelling of 4117142400 in words is "four billion, one hundred seventeen million, one hundred forty-two thousand, four hundred".