648000 has 140 divisors (see below), whose sum is σ = 2397252. Its totient is φ = 172800.

The previous prime is 647987. The next prime is 648007. The reversal of 648000 is 846.

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 20736 + 627264 = 144^2 + 792^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=3, B=60.

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

It is a nialpdrome in base 15.

It is a zygodrome in base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (648007) by changing a digit.

648000 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 19 ways as a sum of consecutive naturals, for example, 129598 + ... + 129602.

2⁶⁴⁸⁰⁰⁰ is an apocalyptic number.

648000 is a gapful number since it is divisible by the number (60) 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 648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1198626).

648000 is an abundant number, since it is smaller than the sum of its proper divisors (1749252).

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

648000 is an equidigital number, since it uses as much as digits as its factorization.

648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 39 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 648000 is about 804.9844718999. The cubic root of 648000 is about 86.5349742184.

648000 divided by its product of nonzero digits (192) gives a cube (3375 = 15³).

Adding to 648000 its reverse (846), we get a palindrome (648846).

It can be divided in two parts, 64 and 8000, that multiplied together give a cube (512000 = 80³).

The spelling of 648000 in words is "six hundred forty-eight thousand".