78249600 has 576 divisors, whose sum is σ = 345290400. Its totient is φ = 16588800.

The previous prime is 78249593. The next prime is 78249629. The reversal of 78249600 is 694287.

78249600 is a `hidden beast` number, since 7 + 8 + 2 + 49 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

It is a super-2 number, since 2×78249600² = 12245999800320000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 4118391 + ... + 4118409.

Almost surely, 2^78249600 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 78249600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (172645200).

78249600 is an abundant number, since it is smaller than the sum of its proper divisors (267040800).

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

78249600 is a wasteful number, since it uses less digits than its factorization.

78249600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 78249600 is about 8845.8803971114. The cubic root of 78249600 is about 427.7211331580.

It can be divided in two parts, 7824 and 9600, that added together give a square (17424 = 132²).

The spelling of 78249600 in words is "seventy-eight million, two hundred forty-nine thousand, six hundred".