48972 has 48 divisors (see below), whose sum is σ = 145152. Its totient is φ = 12480.

The previous prime is 48953. The next prime is 48973. The reversal of 48972 is 27984.

It is not an unprimeable number, because it can be changed into a prime (48973) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 898 + ... + 950.

It is an arithmetic number, because the mean of its divisors is an integer number (3024).

2⁴⁸⁹⁷² is an apocalyptic number.

48972 is a gapful number since it is divisible by the number (42) 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 48972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (72576).

48972 is an abundant number, since it is smaller than the sum of its proper divisors (96180).

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

48972 is a wasteful number, since it uses less digits than its factorization.

48972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 76 counting only the distinct ones).

The product of its digits is 4032, while the sum is 30.

The square root of 48972 is about 221.2961816209. The cubic root of 48972 is about 36.5860856661.

It can be divided in two parts, 489 and 72, that added together give a triangular number (561 = T₃₃).

The spelling of 48972 in words is "forty-eight thousand, nine hundred seventy-two".