7568 has 20 divisors (see below), whose sum is σ = 16368. Its totient is φ = 3360.

The previous prime is 7561. The next prime is 7573. The reversal of 7568 is 8657.

It is a Cunningham number, because it is equal to 87²-1.

Its product of digits (1680) is a multiple of the sum of its prime divisors (56).

It is a plaindrome in base 9 and base 12.

It is not an unprimeable number, because it can be changed into a prime (7561) by changing a digit.

7568 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 3 ways as a sum of consecutive naturals, for example, 155 + ... + 197.

2⁷⁵⁶⁸ is an apocalyptic number.

7568 is the 47-th centered heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7568, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (8184).

7568 is an abundant number, since it is smaller than the sum of its proper divisors (8800).

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

7568 is a wasteful number, since it uses less digits than its factorization.

7568 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 56 counting only the distinct ones).

The product of its digits is 1680, while the sum is 26.

The square root of 7568 is about 86.9942526837. The cubic root of 7568 is about 19.6333183123.

Subtracting 7568 from its reverse (8657), we obtain a square (1089 = 33²).

It can be divided in two parts, 7 and 568, that added together give a palindrome (575).

The spelling of 7568 in words is "seven thousand, five hundred sixty-eight".