75168 has 60 divisors (see below), whose sum is σ = 228690. Its totient is φ = 24192.

The previous prime is 75167. The next prime is 75169. The reversal of 75168 is 86157.

It is an interprime number because it is at equal distance from previous prime (75167) and next prime (75169).

It can be written as a sum of positive squares in only one way, i.e., 63504 + 11664 = 252^2 + 108^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (75161) by changing a digit.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 2578 + ... + 2606.

2⁷⁵¹⁶⁸ 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 75168, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114345).

75168 is an abundant number, since it is smaller than the sum of its proper divisors (153522).

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

75168 is a wasteful number, since it uses less digits than its factorization.

75168 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 34 counting only the distinct ones).

The product of its digits is 1680, while the sum is 27.

The square root of 75168 is about 274.1678318111. The cubic root of 75168 is about 42.2030979360.

It can be divided in two parts, 75 and 168, that added together give a 5-th power (243 = 3⁵).

The spelling of 75168 in words is "seventy-five thousand, one hundred sixty-eight".