67752 has 24 divisors (see below), whose sum is σ = 183690. Its totient is φ = 22560.

The previous prime is 67751. The next prime is 67757. The reversal of 67752 is 25776.

Added to its reverse (25776) it gives a triangular number (93528 = T₄₃₂).

It can be written as a sum of positive squares in only one way, i.e., 54756 + 12996 = 234^2 + 114^2 .

It is a tau number, because it is divible by the number of its divisors (24).

It is not an unprimeable number, because it can be changed into a prime (67751) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 399 + ... + 542.

2⁶⁷⁷⁵² is an apocalyptic number.

It is an amenable number.

67752 is an abundant number, since it is smaller than the sum of its proper divisors (115938).

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

67752 is a wasteful number, since it uses less digits than its factorization.

67752 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 953 (or 946 counting only the distinct ones).

The product of its digits is 2940, while the sum is 27.

The square root of 67752 is about 260.2921435618. The cubic root of 67752 is about 40.7668704533.

Adding to 67752 its reverse (25776), we get a triangular number (93528 = T₄₃₂).

It can be divided in two parts, 677 and 52, that added together give a 6-th power (729 = 3⁶).

The spelling of 67752 in words is "sixty-seven thousand, seven hundred fifty-two".