657072 has 90 divisors (see below), whose sum is σ = 2064972. Its totient is φ = 202176.

The previous prime is 657071. The next prime is 657079. The reversal of 657072 is 270756.

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.

657072 is a `hidden beast` number, since 657 + 0 + 7 + 2 = 666.

It is a super-2 number, since 2×657072² = 863487226368, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (657071) by changing a digit.

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 17 ways as a sum of consecutive naturals, for example, 50538 + ... + 50550.

2⁶⁵⁷⁰⁷² 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 657072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1032486).

657072 is an abundant number, since it is smaller than the sum of its proper divisors (1407900).

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

657072 is a wasteful number, since it uses less digits than its factorization.

657072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 49 (or 18 counting only the distinct ones).

The product of its (nonzero) digits is 2940, while the sum is 27.

The square root of 657072 is about 810.5997779422. The cubic root of 657072 is about 86.9369340808.

Multiplying 657072 by its sum of digits (27), we get a square (17740944 = 4212²).

657072 divided by its sum of digits (27) gives a square (24336 = 156²).

The spelling of 657072 in words is "six hundred fifty-seven thousand, seventy-two".