1948438800 has 900 divisors, whose sum is σ = 8908054848. Its totient is φ = 399168000.

The previous prime is 1948438783. The next prime is 1948438801. The reversal of 1948438800 is 88348491.

1948438800 is a `hidden beast` number, since 194 + 84 + 388 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (900).

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 (1948438801) by changing a digit.

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 179 ways as a sum of consecutive naturals, for example, 27442765 + ... + 27442835.

Almost surely, 2^1948438800 is an apocalyptic number.

1948438800 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 1948438800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4454027424).

1948438800 is an abundant number, since it is smaller than the sum of its proper divisors (6959616048).

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

1948438800 is a wasteful number, since it uses less digits than its factorization.

1948438800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 130 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 45.

The square root of 1948438800 is about 44141.1236830237. The cubic root of 1948438800 is about 1248.9994767095. Note that the first 3 decimals are identical.

The spelling of 1948438800 in words is "one billion, nine hundred forty-eight million, four hundred thirty-eight thousand, eight hundred".