744681600 has 720 divisors, whose sum is σ = 3150727470. Its totient is φ = 172523520.

The previous prime is 744681599. The next prime is 744681653. The reversal of 744681600 is 6186447.

744681600 is a `hidden beast` number, since 7 + 4 + 46 + 8 + 1 + 600 = 666.

It can be written as a sum of positive squares in 9 ways, for example, as 46656 + 744634944 = 216^2 + 27288^2 .

It is a tau number, because it is divible by the number of its divisors (720).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 43804792 + ... + 43804808.

Almost surely, 2^744681600 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 744681600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1575363735).

744681600 is an abundant number, since it is smaller than the sum of its proper divisors (2406045870).

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

744681600 is a wasteful number, since it uses less digits than its factorization.

744681600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 79 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 744681600 is about 27288.8548678760. The cubic root of 744681600 is about 906.4076057244.

The spelling of 744681600 in words is "seven hundred forty-four million, six hundred eighty-one thousand, six hundred".