40001688000 has 784 divisors, whose sum is σ = 156778695840. Its totient is φ = 10105689600.

The previous prime is 40001687993. The next prime is 40001688061. The reversal of 40001688000 is 88610004.

The cubic root of 40001688000 is 3420.

It is a perfect power (a cube), and thus also a powerful number.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 111 ways as a sum of consecutive naturals, for example, 2105351991 + ... + 2105352009.

Almost surely, 2^40001688000 is an apocalyptic number.

40001688000 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 40001688000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (78389347920).

40001688000 is an abundant number, since it is smaller than the sum of its proper divisors (116777007840).

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

40001688000 is an frugal number, since it uses more digits than its factorization.

40001688000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 102 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

Multiplying 40001688000 by its sum of digits (27), we get a cube (1080045576000 = 10260³).

40001688000 divided by its sum of digits (27) gives a cube (1481544000 = 1140³).

The spelling of 40001688000 in words is "forty billion, one million, six hundred eighty-eight thousand".