72546 has 16 divisors (see below), whose sum is σ = 147744. Its totient is φ = 23744.

The previous prime is 72533. The next prime is 72547. The reversal of 72546 is 64527.

It is a happy number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72546.

It is not an unprimeable number, because it can be changed into a prime (72547) by changing a digit.

72546 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, 586 + ... + 698.

It is an arithmetic number, because the mean of its divisors is an integer number (9234).

2⁷²⁵⁴⁶ is an apocalyptic number.

72546 is an abundant number, since it is smaller than the sum of its proper divisors (75198).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (73872).

72546 is a wasteful number, since it uses less digits than its factorization.

72546 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 225.

The product of its digits is 1680, while the sum is 24.

The square root of 72546 is about 269.3436466672. The cubic root of 72546 is about 41.7065715480.

It can be divided in two parts, 7254 and 6, that added together give a triangular number (7260 = T₁₂₀).

The spelling of 72546 in words is "seventy-two thousand, five hundred forty-six".