4688006400 has 972 divisors, whose sum is σ = 21410442144. Its totient is φ = 967680000.

The previous prime is 4688006383. The next prime is 4688006423. The reversal of 4688006400 is 46008864.

4688006400 is a `hidden beast` number, since 4 + 6 + 8 + 8 + 0 + 0 + 640 + 0 = 666.

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 107 ways as a sum of consecutive naturals, for example, 31046325 + ... + 31046475.

Almost surely, 2^4688006400 is an apocalyptic number.

4688006400 is a gapful number since it is divisible by the number (40) 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 4688006400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10705221072).

4688006400 is an abundant number, since it is smaller than the sum of its proper divisors (16722435744).

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

4688006400 is a wasteful number, since it uses less digits than its factorization.

4688006400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 208 (or 179 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 4688006400 is about 68469.0178109778. The cubic root of 4688006400 is about 1673.6426398524.

The spelling of 4688006400 in words is "four billion, six hundred eighty-eight million, six thousand, four hundred".