687416400 has 180 divisors, whose sum is σ = 2602541760. Its totient is φ = 166636800.

The previous prime is 687416393. The next prime is 687416419. The reversal of 687416400 is 4614786.

687416400 is a `hidden beast` number, since 6 + 8 + 7 + 4 + 1 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (180).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 30921 + ... + 48279.

Almost surely, 2^687416400 is an apocalyptic number.

687416400 is a gapful number since it is divisible by the number (60) 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 687416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1301270880).

687416400 is an abundant number, since it is smaller than the sum of its proper divisors (1915125360).

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

687416400 is a wasteful number, since it uses less digits than its factorization.

687416400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 17394 (or 17380 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The square root of 687416400 is about 26218.6269663383. The cubic root of 687416400 is about 882.5513081849.

The spelling of 687416400 in words is "six hundred eighty-seven million, four hundred sixteen thousand, four hundred".