72680 has 32 divisors (see below), whose sum is σ = 172800. Its totient is φ = 27456.

The previous prime is 72679. The next prime is 72689. The reversal of 72680 is 8627.

72680 = T₁₆₈ + T₁₆₉ + ... + T₁₇₂.

It is a Harshad number since it is a multiple of its sum of digits (23).

It is not an unprimeable number, because it can be changed into a prime (72689) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 881 + ... + 959.

It is an arithmetic number, because the mean of its divisors is an integer number (5400).

2⁷²⁶⁸⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (86400).

72680 is an abundant number, since it is smaller than the sum of its proper divisors (100120).

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

72680 is a wasteful number, since it uses less digits than its factorization.

72680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 113 (or 109 counting only the distinct ones).

The product of its (nonzero) digits is 672, while the sum is 23.

The square root of 72680 is about 269.5922847561. The cubic root of 72680 is about 41.7322345441.

72680 divided by its sum of digits (23) gives a triangular number (3160 = T₇₉).

The spelling of 72680 in words is "seventy-two thousand, six hundred eighty".