409138797600 has 1152 divisors, whose sum is σ = 1685142144000. Its totient is φ = 95080366080.

The previous prime is 409138797523. The next prime is 409138797607. The reversal of 409138797600 is 6797831904.

It is a happy number.

409138797600 is a `hidden beast` number, since 409 + 13 + 87 + 97 + 60 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is not an unprimeable number, because it can be changed into a prime (409138797607) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 382729866 + ... + 382730934.

It is an arithmetic number, because the mean of its divisors is an integer number (1462797000).

Almost surely, 2^409138797600 is an apocalyptic number.

409138797600 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 409138797600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (842571072000).

409138797600 is an abundant number, since it is smaller than the sum of its proper divisors (1276003346400).

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

409138797600 is a wasteful number, since it uses less digits than its factorization.

409138797600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1187 (or 1168 counting only the distinct ones).

The product of its (nonzero) digits is 2286144, while the sum is 54.

The spelling of 409138797600 in words is "four hundred nine billion, one hundred thirty-eight million, seven hundred ninety-seven thousand, six hundred".