37152 has 48 divisors (see below), whose sum is σ = 110880. Its totient is φ = 12096.

The previous prime is 37139. The next prime is 37159. The reversal of 37152 is 25173.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-2 number, since 2×37152² = 2760542208, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 37152.

It is not an unprimeable number, because it can be changed into a prime (37159) by changing a digit.

37152 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 7 ways as a sum of consecutive naturals, for example, 843 + ... + 885.

It is an arithmetic number, because the mean of its divisors is an integer number (2310).

2³⁷¹⁵² is an apocalyptic number.

37152 is a gapful number since it is divisible by the number (32) 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 37152, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (55440).

37152 is an abundant number, since it is smaller than the sum of its proper divisors (73728).

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

37152 is a wasteful number, since it uses less digits than its factorization.

37152 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 48 counting only the distinct ones).

The product of its digits is 210, while the sum is 18.

The square root of 37152 is about 192.7485408505. The cubic root of 37152 is about 33.3677865991.

The spelling of 37152 in words is "thirty-seven thousand, one hundred fifty-two".