34538400 has 360 divisors, whose sum is σ = 138952044. Its totient is φ = 8294400.

The previous prime is 34538393. The next prime is 34538429. The reversal of 34538400 is 483543.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 944784 + 33593616 = 972^2 + 5796^2 .

It is a tau number, because it is divible by the number of its divisors (360).

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

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 842380 + ... + 842420.

Almost surely, 2^34538400 is an apocalyptic number.

34538400 is a gapful number since it is divisible by the number (30) 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 34538400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (69476022).

34538400 is an abundant number, since it is smaller than the sum of its proper divisors (104413644).

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

34538400 is a wasteful number, since it uses less digits than its factorization.

34538400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 5760, while the sum is 27.

The square root of 34538400 is about 5876.9379782332. The cubic root of 34538400 is about 325.6622394085.

34538400 divided by its sum of digits (27) gives a triangular number (1279200 = T₁₅₉₉).

The spelling of 34538400 in words is "thirty-four million, five hundred thirty-eight thousand, four hundred".