7961408000 has 320 divisors, whose sum is σ = 24451435008. Its totient is φ = 2517811200.

The previous prime is 7961407981. The next prime is 7961408009. The reversal of 7961408000 is 8041697.

It is a tau number, because it is divible by the number of its divisors (320).

It is a hoax number, since the sum of its digits (35) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (35).

It is not an unprimeable number, because it can be changed into a prime (7961408009) by changing a digit.

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 31 ways as a sum of consecutive naturals, for example, 5823317 + ... + 5824683.

Almost surely, 2^7961408000 is an apocalyptic number.

7961408000 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 7961408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (12225717504).

7961408000 is an abundant number, since it is smaller than the sum of its proper divisors (16490027008).

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

7961408000 is a wasteful number, since it uses less digits than its factorization.

7961408000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1420 (or 1394 counting only the distinct ones).

The product of its (nonzero) digits is 12096, while the sum is 35.

The square root of 7961408000 is about 89226.7224546548. The cubic root of 7961408000 is about 1996.7788147681.

Adding to 7961408000 its reverse (8041697), we get a palindrome (7969449697).

The spelling of 7961408000 in words is "seven billion, nine hundred sixty-one million, four hundred eight thousand".