688193157731040 has 1920 divisors, whose sum is σ = 2885669169546240. Its totient is φ = 152827940339712.

The previous prime is 688193157731029. The next prime is 688193157731077. The reversal of 688193157731040 is 40137751391886.

688193157731040 is a `hidden beast` number, since 6 + 8 + 8 + 1 + 9 + 3 + 1 + 577 + 3 + 10 + 40 = 666.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 319 ways as a sum of consecutive naturals, for example, 16713026932 + ... + 16713068108.

It is an arithmetic number, because the mean of its divisors is an integer number (1502952692472).

Almost surely, 2^{688193157731040} is an apocalyptic number.

688193157731040 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 688193157731040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1442834584773120).

688193157731040 is an abundant number, since it is smaller than the sum of its proper divisors (2197476011815200).

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

688193157731040 is a wasteful number, since it uses less digits than its factorization.

688193157731040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41486 (or 41469 counting only the distinct ones).

The product of its (nonzero) digits is 30481920, while the sum is 63.

The spelling of 688193157731040 in words is "six hundred eighty-eight trillion, one hundred ninety-three billion, one hundred fifty-seven million, seven hundred thirty-one thousand, forty".