37500 has 36 divisors (see below), whose sum is σ = 109368. Its totient is φ = 10000.

The previous prime is 37493. The next prime is 37501. The reversal of 37500 is 573.

37500 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 5.

It is a zygodrome in base 5.

It is a self number, because there is not a number n which added to its sum of digits gives 37500.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (37501) by changing a digit.

37500 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 7498 + ... + 7502.

It is an arithmetic number, because the mean of its divisors is an integer number (3038).

2³⁷⁵⁰⁰ is an apocalyptic number.

37500 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 37500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (54684).

37500 is an abundant number, since it is smaller than the sum of its proper divisors (71868).

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

37500 is an equidigital number, since it uses as much as digits as its factorization.

37500 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 105, while the sum is 15.

The square root of 37500 is about 193.6491673104. The cubic root of 37500 is about 33.4716475041.

Multiplying 37500 by its sum of digits (15), we get a square (562500 = 750²).

37500 divided by its sum of digits (15) gives a square (2500 = 50²).

It can be divided in two parts, 3 and 7500, that multiplied together give a square (22500 = 150²).

The spelling of 37500 in words is "thirty-seven thousand, five hundred".