542416089600 has 2880 divisors, whose sum is σ = 2672416454400. Its totient is φ = 105106636800.

The previous prime is 542416089599. The next prime is 542416089601. The reversal of 542416089600 is 6980614245.

542416089600 is a `hidden beast` number, since 5 + 4 + 24 + 16 + 0 + 8 + 9 + 600 = 666.

It is an interprime number because it is at equal distance from previous prime (542416089599) and next prime (542416089601).

It is a tau number, because it is divible by the number of its divisors (2880).

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

It is not an unprimeable number, because it can be changed into a prime (542416089601) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 4976294346 + ... + 4976294454.

It is an arithmetic number, because the mean of its divisors is an integer number (927922380).

Almost surely, 2^542416089600 is an apocalyptic number.

542416089600 is a gapful number since it is divisible by the number (50) 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 542416089600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1336208227200).

542416089600 is an abundant number, since it is smaller than the sum of its proper divisors (2130000364800).

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

542416089600 is a wasteful number, since it uses less digits than its factorization.

542416089600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 192 (or 154 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 542416089600 in words is "five hundred forty-two billion, four hundred sixteen million, eighty-nine thousand, six hundred".