657 has 6 divisors (see below), whose sum is σ = 962. Its totient is φ = 432.

The previous prime is 653. The next prime is 659. The reversal of 657 is 756.

657 is nontrivially palindromic in base 8.

It can be written as a sum of positive squares in only one way, i.e., 576 + 81 = 24^2 + 9^2 .

It is not a de Polignac number, because 657 - 2^{2} = 653 is a prime.

It is a Duffinian number.

It is a plaindrome in base 12 and base 14.

It is a nialpdrome in base 9.

It is not an unprimeable number, because it can be changed into a prime (653) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 28 + ... + 45.

It is an amenable number.

657 is a deficient number, since it is larger than the sum of its proper divisors (305).

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

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

The sum of its prime factors is 79 (or 76 counting only the distinct ones).

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

The square root of 657 is about 25.6320112360. The cubic root of 657 is about 8.6933758534.

Subtracting 657 from its reverse (756), we obtain a palindrome (99).

The spelling of 657 in words is "six hundred fifty-seven", and thus it is an aban number and an oban number.

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