48672 has 54 divisors (see below), whose sum is σ = 149877. Its totient is φ = 14976.

The previous prime is 48661. The next prime is 48673. The reversal of 48672 is 27684.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 41616 + 7056 = 204^2 + 84^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=156.

Its product of digits (2688) is a multiple of the sum of its prime factors (42).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 48672.

It is not an unprimeable number, because it can be changed into a prime (48673) by changing a digit.

48672 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 3738 + ... + 3750.

48672 is a Friedman number, since it can be written as 624*78, using all its digits and the basic arithmetic operations.

2⁴⁸⁶⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 48672

48672 is an abundant number, since it is smaller than the sum of its proper divisors (101205).

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

48672 is a wasteful number, since it uses less digits than its factorization.

48672 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 42 (or 18 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 48672 is about 220.6173157302. The cubic root of 48672 is about 36.5112244206.

Adding to 48672 its product of digits (2688), we get a triangular number (51360 = T₃₂₀).

The spelling of 48672 in words is "forty-eight thousand, six hundred seventy-two".