68640 has 96 divisors (see below), whose sum is σ = 254016. Its totient is φ = 15360.

The previous prime is 68639. The next prime is 68659. The reversal of 68640 is 4686.

It is a tau number, because it is divible by the number of its divisors (96).

It is a super-2 number, since 2×68640² = 9422899200, which contains 22 as substring.

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a d-powerful number, because it can be written as 6⁴ + 8³ + 6⁴ + 4⁸ + 0 .

It is a self number, because there is not a number n which added to its sum of digits gives 68640.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 5274 + ... + 5286.

It is an arithmetic number, because the mean of its divisors is an integer number (2646).

2⁶⁸⁶⁴⁰ is an apocalyptic number.

68640 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 68640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (127008).

68640 is an abundant number, since it is smaller than the sum of its proper divisors (185376).

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

68640 is a wasteful number, since it uses less digits than its factorization.

68640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 24.

The square root of 68640 is about 261.9923663010. The cubic root of 68640 is about 40.9442032999.

It can be divided in two parts, 6 and 8640, that added together give a triangular number (8646 = T₁₃₁).

The spelling of 68640 in words is "sixty-eight thousand, six hundred forty".