88800 has 72 divisors (see below), whose sum is σ = 296856. Its totient is φ = 23040.

The previous prime is 88799. The next prime is 88801. The reversal of 88800 is 888.

It is a happy number.

88800 is nontrivially palindromic in base 7.

It is an interprime number because it is at equal distance from previous prime (88799) and next prime (88801).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 10.

It is a zygodrome in base 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (88801) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2382 + ... + 2418.

It is an arithmetic number, because the mean of its divisors is an integer number (4123).

2^{88800} is an apocalyptic number.

88800 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 88800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148428).

88800 is an abundant number, since it is smaller than the sum of its proper divisors (208056).

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

88800 is a wasteful number, since it uses less digits than its factorization.

88800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 60 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 512, while the sum is 24.

The square root of 88800 is about 297.9932885150. The cubic root of 88800 is about 44.6139820895.

Subtracting from 88800 its product of nonzero digits (512), we obtain a palindrome (88288).

Multiplying 88800 by its reverse (888), we get a square (78854400 = 8880^{2}).

88800 divided by its reverse (888) gives a square (100 = 10^{2}).

It can be divided in two parts, 88 and 800, that added together give a palindrome (888).

The spelling of 88800 in words is "eighty-eight thousand, eight hundred".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 37 40 48 50 60 74 75 80 96 100 111 120 148 150 160 185 200 222 240 296 300 370 400 444 480 555 592 600 740 800 888 925 1110 1184 1200 1480 1776 1850 2220 2400 2775 2960 3552 3700 4440 5550 5920 7400 8880 11100 14800 17760 22200 29600 44400 88800

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