2638400 has 84 divisors (see below), whose sum is σ = 6944868. Its totient is φ = 983040.

The previous prime is 2638381. The next prime is 2638403. The reversal of 2638400 is 48362.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 1024 + 2637376 = 32^2 + 1624^2 .

It is a super-2 number, since 2×2638400² = 13922309120000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (2638403) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 27152 + ... + 27248.

It is an arithmetic number, because the mean of its divisors is an integer number (82677).

2^2638400 is an apocalyptic number.

2638400 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 2638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3472434).

2638400 is an abundant number, since it is smaller than the sum of its proper divisors (4306468).

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

2638400 is a wasteful number, since it uses less digits than its factorization.

2638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 136 (or 121 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 23.

The square root of 2638400 is about 1624.3152403398. The cubic root of 2638400 is about 138.1805380558.

The spelling of 2638400 in words is "two million, six hundred thirty-eight thousand, four hundred".