87814400 has 54 divisors (see below), whose sum is σ = 217370202. Its totient is φ = 35123200.

The previous prime is 87814399. The next prime is 87814429. The reversal of 87814400 is 441878.

It can be written as a sum of positive squares in 3 ways, for example, as 802816 + 87011584 = 896^2 + 9328^2 .

It is a super-2 number, since 2×87814400² = 15422737694720000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 461 + ... + 13260.

Almost surely, 2^87814400 is an apocalyptic number.

87814400 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 87814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108685101).

87814400 is an abundant number, since it is smaller than the sum of its proper divisors (129555802).

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

87814400 is a wasteful number, since it uses less digits than its factorization.

87814400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 13747 (or 13728 counting only the distinct ones).

The product of its (nonzero) digits is 7168, while the sum is 32.

The square root of 87814400 is about 9370.9337848477. The cubic root of 87814400 is about 444.4830929354.

The spelling of 87814400 in words is "eighty-seven million, eight hundred fourteen thousand, four hundred".