7564 has 12 divisors (see below), whose sum is σ = 13888. Its totient is φ = 3600.

The previous prime is 7561. The next prime is 7573. The reversal of 7564 is 4657.

7564 is an undulating number in base 11.

It is a plaindrome in base 9 and base 13.

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

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 94 + ... + 154.

2⁷⁵⁶⁴ is an apocalyptic number.

It is an amenable number.

7564 is a deficient number, since it is larger than the sum of its proper divisors (6324).

7564 is a wasteful number, since it uses less digits than its factorization.

7564 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 96 (or 94 counting only the distinct ones).

The product of its digits is 840, while the sum is 22.

The square root of 7564 is about 86.9712596206. The cubic root of 7564 is about 19.6298586967.

Subtracting from 7564 its product of digits (840), we obtain a square (6724 = 82²).

Adding to 7564 its reverse (4657), we get a palindrome (12221).

The spelling of 7564 in words is "seven thousand, five hundred sixty-four".