27842400 has 144 divisors (see below), whose sum is σ = 100774800. Its totient is φ = 7418880.

The previous prime is 27842393. The next prime is 27842401. The reversal of 27842400 is 424872.

It is a tau number, because it is divible by the number of its divisors (144).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (27842401) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 20956 + ... + 22244.

It is an arithmetic number, because the mean of its divisors is an integer number (699825).

Almost surely, 2^27842400 is an apocalyptic number.

27842400 is a gapful number since it is divisible by the number (20) 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 27842400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50387400).

27842400 is an abundant number, since it is smaller than the sum of its proper divisors (72932400).

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

27842400 is a wasteful number, since it uses less digits than its factorization.

27842400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1318 (or 1299 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 27842400 is about 5276.5898078210. The cubic root of 27842400 is about 303.0881029947.

It can be divided in two parts, 2784 and 2400, that added together give a square (5184 = 72²).

The spelling of 27842400 in words is "twenty-seven million, eight hundred forty-two thousand, four hundred".