681732000 has 288 divisors, whose sum is σ = 2506729680. Its totient is φ = 175257600.

The previous prime is 681731959. The next prime is 681732013. The reversal of 681732000 is 237186.

It can be written as a sum of positive squares in 8 ways, for example, as 1774224 + 679957776 = 1332^2 + 26076^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1043674 + ... + 1044326.

Almost surely, 2^681732000 is an apocalyptic number.

681732000 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 681732000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1253364840).

681732000 is an abundant number, since it is smaller than the sum of its proper divisors (1824997680).

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

681732000 is a wasteful number, since it uses less digits than its factorization.

681732000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 713 (or 692 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 681732000 is about 26109.9980850248. The cubic root of 681732000 is about 880.1119003708. Note that the first 3 decimals are identical.

Adding to 681732000 its reverse (237186), we get a palindrome (681969186).

The spelling of 681732000 in words is "six hundred eighty-one million, seven hundred thirty-two thousand".