76876800 has 528 divisors, whose sum is σ = 341144832. Its totient is φ = 14745600.

The previous prime is 76876799. The next prime is 76876801. The reversal of 76876800 is 867867.

It is an interprime number because it is at equal distance from previous prime (76876799) and next prime (76876801).

It is a tau number, because it is divible by the number of its divisors (528).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (76876801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5913594 + ... + 5913606.

Almost surely, 2^76876800 is an apocalyptic number.

76876800 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 76876800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (170572416).

76876800 is an abundant number, since it is smaller than the sum of its proper divisors (264268032).

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

76876800 is a wasteful number, since it uses less digits than its factorization.

76876800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 64 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 112896, while the sum is 42.

The square root of 76876800 is about 8767.9416056450. The cubic root of 76876800 is about 425.2050682792.

Multiplying 76876800 by its reverse (867867), we get a square (66718837785600 = 8168160²).

It can be divided in two parts, 768 and 76800, that multiplied together give a square (58982400 = 7680²).

The spelling of 76876800 in words is "seventy-six million, eight hundred seventy-six thousand, eight hundred".