1077138000 has 400 divisors, whose sum is σ = 3990763920. Its totient is φ = 279936000.

The previous prime is 1077137993. The next prime is 1077138017. The reversal of 1077138000 is 8317701.

It can be written as a sum of positive squares in 8 ways, for example, as 561121344 + 516016656 = 23688^2 + 22716^2 .

It is a tau number, because it is divible by the number of its divisors (400).

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 9881946 + ... + 9882054.

Almost surely, 2^1077138000 is an apocalyptic number.

1077138000 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 1077138000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1995381960).

1077138000 is an abundant number, since it is smaller than the sum of its proper divisors (2913625920).

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

1077138000 is a wasteful number, since it uses less digits than its factorization.

1077138000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 205 (or 180 counting only the distinct ones).

The product of its (nonzero) digits is 1176, while the sum is 27.

The square root of 1077138000 is about 32819.7806208390. The cubic root of 1077138000 is about 1025.0784790199.

The spelling of 1077138000 in words is "one billion, seventy-seven million, one hundred thirty-eight thousand".