1948144800 has 288 divisors, whose sum is σ = 7369778304. Its totient is φ = 437760000.

The previous prime is 1948144769. The next prime is 1948144817. The reversal of 1948144800 is 84418491.

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 47 ways as a sum of consecutive naturals, for example, 1023850 + ... + 1025750.

It is an arithmetic number, because the mean of its divisors is an integer number (25589508).

Almost surely, 2^1948144800 is an apocalyptic number.

1948144800 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 1948144800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3684889152).

1948144800 is an abundant number, since it is smaller than the sum of its proper divisors (5421633504).

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

1948144800 is a wasteful number, since it uses less digits than its factorization.

1948144800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1992 (or 1979 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 39.

The square root of 1948144800 is about 44137.7933295266. The cubic root of 1948144800 is about 1248.9366530244.

The spelling of 1948144800 in words is "one billion, nine hundred forty-eight million, one hundred forty-four thousand, eight hundred".