657968 has 40 divisors (see below), whose sum is σ = 1406160. Its totient is φ = 296960.

The previous prime is 657959. The next prime is 657973. The reversal of 657968 is 869756.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (41).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 657968.

It is an unprimeable number.

657968 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 7 ways as a sum of consecutive naturals, for example, 11123 + ... + 11181.

It is an arithmetic number, because the mean of its divisors is an integer number (35154).

2⁶⁵⁷⁹⁶⁸ is an apocalyptic number.

657968 is a gapful number since it is divisible by the number (68) 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 657968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (703080).

657968 is an abundant number, since it is smaller than the sum of its proper divisors (748192).

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

657968 is a wasteful number, since it uses less digits than its factorization.

657968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 125 (or 119 counting only the distinct ones).

The product of its digits is 90720, while the sum is 41.

The square root of 657968 is about 811.1522668402. The cubic root of 657968 is about 86.9764326000.

The spelling of 657968 in words is "six hundred fifty-seven thousand, nine hundred sixty-eight".