77948640 has 576 divisors, whose sum is σ = 358525440. Its totient is φ = 14929920.

The previous prime is 77948639. The next prime is 77948653. The reversal of 77948640 is 4684977.

77948640 = T₁₁₂ + T₁₁₃ + ... + T₇₇₆.

It is a super-3 number, since 3×77948640³ (a number of 25 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 2106702 + ... + 2106738.

It is an arithmetic number, because the mean of its divisors is an integer number (622440).

Almost surely, 2^77948640 is an apocalyptic number.

77948640 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 77948640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179262720).

77948640 is an abundant number, since it is smaller than the sum of its proper divisors (280576800).

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

77948640 is a wasteful number, since it uses less digits than its factorization.

77948640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 95 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 338688, while the sum is 45.

The square root of 77948640 is about 8828.8527000964. The cubic root of 77948640 is about 427.1720681986.

The spelling of 77948640 in words is "seventy-seven million, nine hundred forty-eight thousand, six hundred forty".