842400 has 180 divisors, whose sum is σ = 3308382. Its totient is φ = 207360.

The previous prime is 842399. The next prime is 842407. The reversal of 842400 is 4248.

842400 = T₂₄₇ + T₂₄₈ + ... + T₂₇₁.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 467856 + 374544 = 684^2 + 612^2 .

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an Ulam number.

It is a zygodrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (842407) by changing a digit.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 64794 + ... + 64806.

2⁸⁴²⁴⁰⁰ is an apocalyptic number.

842400 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 842400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1654191).

842400 is an abundant number, since it is smaller than the sum of its proper divisors (2465982).

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

842400 is a wasteful number, since it uses less digits than its factorization.

842400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 45 (or 23 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 18.

The square root of 842400 is about 917.8235124467. The cubic root of 842400 is about 94.4436549979.

Adding to 842400 its reverse (4248), we get a palindrome (846648).

The spelling of 842400 in words is "eight hundred forty-two thousand, four hundred".