34164000 has 288 divisors, whose sum is σ = 132363504. Its totient is φ = 8294400.

The previous prime is 34163981. The next prime is 34164007. The reversal of 34164000 is 46143.

It can be written as a sum of positive squares in 8 ways, for example, as 11664 + 34152336 = 108^2 + 5844^2 .

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (34164007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 467964 + ... + 468036.

Almost surely, 2^34164000 is an apocalyptic number.

34164000 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 34164000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (66181752).

34164000 is an abundant number, since it is smaller than the sum of its proper divisors (98199504).

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

34164000 is a wasteful number, since it uses less digits than its factorization.

34164000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 117 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 34164000 is about 5844.9978614196. The cubic root of 34164000 is about 324.4812236337.

The spelling of 34164000 in words is "thirty-four million, one hundred sixty-four thousand".