31968000 has 288 divisors, whose sum is σ = 121168320. Its totient is φ = 8294400.

The previous prime is 31967989. The next prime is 31968011. The reversal of 31968000 is 86913.

It is an interprime number because it is at equal distance from previous prime (31967989) and next prime (31968011).

It is a tau number, because it is divible by the number of its divisors (288).

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

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 863982 + ... + 864018.

Almost surely, 2^31968000 is an apocalyptic number.

31968000 is a gapful number since it is divisible by the number (30) 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 31968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (60584160).

31968000 is an abundant number, since it is smaller than the sum of its proper divisors (89200320).

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

31968000 is an equidigital number, since it uses as much as digits as its factorization.

31968000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 77 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 31968000 is about 5654.0251149071. The cubic root of 31968000 is about 317.3743483617.

The spelling of 31968000 in words is "thirty-one million, nine hundred sixty-eight thousand".