1138406400 has 462 divisors, whose sum is σ = 4300227062. Its totient is φ = 298598400.

The previous prime is 1138406393. The next prime is 1138406407. The reversal of 1138406400 is 46048311.

1138406400 is a `hidden beast` number, since 1 + 13 + 8 + 4 + 0 + 640 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (1138406393) and next prime (1138406407).

It can be written as a sum of positive squares in 3 ways, for example, as 2985984 + 1135420416 = 1728^2 + 33696^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1138406407) by changing a digit.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 18662370 + ... + 18662430.

Almost surely, 2^1138406400 is an apocalyptic number.

1138406400 is a gapful number since it is divisible by the number (10) 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 1138406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2150113531).

1138406400 is an abundant number, since it is smaller than the sum of its proper divisors (3161820662).

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

1138406400 is an frugal number, since it uses more digits than its factorization.

1138406400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 109 (or 71 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 1138406400 is about 33740.2785999167. The cubic root of 1138406400 is about 1044.1569324137.

The spelling of 1138406400 in words is "one billion, one hundred thirty-eight million, four hundred six thousand, four hundred".