77531126400 has 1920 divisors, whose sum is σ = 372807388800. Its totient is φ = 15407677440.

The previous prime is 77531126399. The next prime is 77531126423. The reversal of 77531126400 is 462113577.

It is a happy number.

77531126400 is a `hidden beast` number, since 7 + 7 + 5 + 3 + 1 + 1 + 2 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

It is a super-2 number, since 2×77531126400² (a number of 23 digits) 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 polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 448156714 + ... + 448156886.

It is an arithmetic number, because the mean of its divisors is an integer number (194170515).

Almost surely, 2^77531126400 is an apocalyptic number.

77531126400 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 77531126400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (186403694400).

77531126400 is an abundant number, since it is smaller than the sum of its proper divisors (295276262400).

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

77531126400 is a wasteful number, since it uses less digits than its factorization.

77531126400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 248 (or 222 counting only the distinct ones).

The product of its (nonzero) digits is 35280, while the sum is 36.

Adding to 77531126400 its reverse (462113577), we get a palindrome (77993239977).

The spelling of 77531126400 in words is "seventy-seven billion, five hundred thirty-one million, one hundred twenty-six thousand, four hundred".