1688678400 has 312 divisors, whose sum is σ = 5850339840. Its totient is φ = 428933120.

The previous prime is 1688678399. The next prime is 1688678401. The reversal of 1688678400 is 48768861.

It is an interprime number because it is at equal distance from previous prime (1688678399) and next prime (1688678401).

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 1688678400.

It is not an unprimeable number, because it can be changed into a prime (1688678401) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 7065481 + ... + 7065719.

Almost surely, 2^1688678400 is an apocalyptic number.

1688678400 is a gapful number since it is divisible by the number (10) 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 1688678400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2925169920).

1688678400 is an abundant number, since it is smaller than the sum of its proper divisors (4161661440).

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

1688678400 is a wasteful number, since it uses less digits than its factorization.

1688678400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 299 (or 272 counting only the distinct ones).

The product of its (nonzero) digits is 516096, while the sum is 48.

The square root of 1688678400 is about 41093.5323378266. The cubic root of 1688678400 is about 1190.8278494428.

The spelling of 1688678400 in words is "one billion, six hundred eighty-eight million, six hundred seventy-eight thousand, four hundred".