7640942400 has 1260 divisors, whose sum is σ = 36126211212. Its totient is φ = 1517322240.

The previous prime is 7640942399. The next prime is 7640942431. The reversal of 7640942400 is 42490467.

7640942400 is a `hidden beast` number, since 7 + 6 + 409 + 4 + 240 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 271063296 + 7369879104 = 16464^2 + 85848^2 .

It is a tau number, because it is divible by the number of its divisors (1260).

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 (17) of ones.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 449467192 + ... + 449467208.

Almost surely, 2^7640942400 is an apocalyptic number.

7640942400 is a gapful number since it is divisible by the number (70) 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 7640942400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18063105606).

7640942400 is an abundant number, since it is smaller than the sum of its proper divisors (28485268812).

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

7640942400 is a wasteful number, since it uses less digits than its factorization.

7640942400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 86 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 36.

The square root of 7640942400 is about 87412.4842342328. The cubic root of 7640942400 is about 1969.6193789980.

The spelling of 7640942400 in words is "seven billion, six hundred forty million, nine hundred forty-two thousand, four hundred".