77738400 has 288 divisors, whose sum is σ = 290606400. Its totient is φ = 20044800.

The previous prime is 77738317. The next prime is 77738407. The reversal of 77738400 is 483777.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is not an unprimeable number, because it can be changed into a prime (77738407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1274370 + ... + 1274430.

It is an arithmetic number, because the mean of its divisors is an integer number (1009050).

Almost surely, 2^77738400 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 77738400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145303200).

77738400 is an abundant number, since it is smaller than the sum of its proper divisors (212868000).

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

77738400 is a wasteful number, since it uses less digits than its factorization.

77738400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 149 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 32928, while the sum is 36.

The square root of 77738400 is about 8816.9382440845. The cubic root of 77738400 is about 426.7876718422.

The spelling of 77738400 in words is "seventy-seven million, seven hundred thirty-eight thousand, four hundred".