10638400 has 84 divisors (see below), whose sum is σ = 26850340. Its totient is φ = 4147200.

The previous prime is 10638391. The next prime is 10638421. The reversal of 10638400 is 483601.

It can be written as a sum of positive squares in 6 ways, for example, as 1201216 + 9437184 = 1096^2 + 3072^2 .

It is a super-2 number, since 2×10638400² = 226351109120000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 97546 + ... + 97654.

Almost surely, 2^10638400 is an apocalyptic number.

10638400 is a gapful number since it is divisible by the number (10) 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 10638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13425170).

10638400 is an abundant number, since it is smaller than the sum of its proper divisors (16211940).

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

10638400 is a wasteful number, since it uses less digits than its factorization.

10638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 192 (or 177 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The square root of 10638400 is about 3261.6560211034. The cubic root of 10638400 is about 219.9338644181.

The spelling of 10638400 in words is "ten million, six hundred thirty-eight thousand, four hundred".