37968000 has 256 divisors, whose sum is σ = 145117440. Its totient is φ = 8601600.

The previous prime is 37967999. The next prime is 37968001. The reversal of 37968000 is 86973.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (37967999) and next prime (37968001).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (37968001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 335944 + ... + 336056.

It is an arithmetic number, because the mean of its divisors is an integer number (566865).

Almost surely, 2^37968000 is an apocalyptic number.

37968000 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 37968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (72558720).

37968000 is an abundant number, since it is smaller than the sum of its proper divisors (107149440).

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

37968000 is a wasteful number, since it uses less digits than its factorization.

37968000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 152 (or 130 counting only the distinct ones).

The product of its (nonzero) digits is 9072, while the sum is 33.

The square root of 37968000 is about 6161.8179135706. The cubic root of 37968000 is about 336.1031429378.

The spelling of 37968000 in words is "thirty-seven million, nine hundred sixty-eight thousand".