7752 has 32 divisors (see below), whose sum is σ = 21600. Its totient is φ = 2304.

The previous prime is 7741. The next prime is 7753. The reversal of 7752 is 2577.

7752 is nontrivially palindromic in base 7.

It is a super-4 number, since 4×7752⁴ = 14444916891992064, which contains 4444 as substring.

It is an Ulam number.

It is a plaindrome in base 15.

It is a nialpdrome in base 6 and base 10.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 7752.

It is not an unprimeable number, because it can be changed into a prime (7753) by changing a digit.

7752 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, 399 + ... + 417.

It is an arithmetic number, because the mean of its divisors is an integer number (675).

2⁷⁷⁵² 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 7752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10800).

7752 is an abundant number, since it is smaller than the sum of its proper divisors (13848).

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

7752 is a wasteful number, since it uses less digits than its factorization.

7752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45 (or 41 counting only the distinct ones).

The product of its digits is 490, while the sum is 21.

The square root of 7752 is about 88.0454428122. The cubic root of 7752 is about 19.7911602210.

It can be divided in two parts, 775 and 2, that added together give a palindrome (777).

The spelling of 7752 in words is "seven thousand, seven hundred fifty-two".