7401038400 has 756 divisors, whose sum is σ = 32452234308. Its totient is φ = 1589575680.

The previous prime is 7401038341. The next prime is 7401038401. The reversal of 7401038400 is 48301047.

It can be written as a sum of positive squares in 6 ways, for example, as 652087296 + 6748951104 = 25536^2 + 82152^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7401038401) 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 107 ways as a sum of consecutive naturals, for example, 11994892 + ... + 11995508.

Almost surely, 2^7401038400 is an apocalyptic number.

7401038400 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 7401038400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16226117154).

7401038400 is an abundant number, since it is smaller than the sum of its proper divisors (25051195908).

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

7401038400 is a wasteful number, since it uses less digits than its factorization.

7401038400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 676 (or 651 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 7401038400 is about 86029.2880361101. The cubic root of 7401038400 is about 1948.7863058887.

Adding to 7401038400 its reverse (48301047), we get a palindrome (7449339447).

The spelling of 7401038400 in words is "seven billion, four hundred one million, thirty-eight thousand, four hundred".