152006414400 has 735 divisors, whose sum is σ = 591944379101. Its totient is φ = 38401620480.

The previous prime is 152006414383. The next prime is 152006414411. The reversal of 152006414400 is 4414600251.

The square root of 152006414400 is 389880.

It is a perfect power (a square), and thus also a powerful number.

152006414400 is a `hidden beast` number, since 1 + 5 + 200 + 6 + 414 + 40 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 54722309184 + 97284105216 = 233928^2 + 311904^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 104 ways as a sum of consecutive naturals, for example, 8000337591 + ... + 8000337609.

Almost surely, 2^152006414400 is an apocalyptic number.

152006414400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

152006414400 is the 389880-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 152006414400

152006414400 is an abundant number, since it is smaller than the sum of its proper divisors (439937964701).

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

152006414400 is an frugal number, since it uses more digits than its factorization.

152006414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 116 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The spelling of 152006414400 in words is "one hundred fifty-two billion, six million, four hundred fourteen thousand, four hundred".