81948000 has 96 divisors (see below), whose sum is σ = 268500960. Its totient is φ = 21849600.

The previous prime is 81947989. The next prime is 81948023. The reversal of 81948000 is 84918.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 8586 + ... + 15414.

It is an arithmetic number, because the mean of its divisors is an integer number (2796885).

Almost surely, 2^81948000 is an apocalyptic number.

81948000 is a gapful number since it is divisible by the number (80) 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 81948000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134250480).

81948000 is an abundant number, since it is smaller than the sum of its proper divisors (186552960).

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

81948000 is a wasteful number, since it uses less digits than its factorization.

81948000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 6857 (or 6839 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 30.

The square root of 81948000 is about 9052.5134631217. The cubic root of 81948000 is about 434.3562945898.

The spelling of 81948000 in words is "eighty-one million, nine hundred forty-eight thousand".