7644 has 36 divisors (see below), whose sum is σ = 22344. Its totient is φ = 2016.

The previous prime is 7643. The next prime is 7649. The reversal of 7644 is 4467.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a nude number because it is divisible by every one of its digits.

It is a nialpdrome in base 6 and base 10.

It is a self number, because there is not a number n which added to its sum of digits gives 7644.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7643) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 582 + ... + 594.

2⁷⁶⁴⁴ 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 7644, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (11172).

7644 is an abundant number, since it is smaller than the sum of its proper divisors (14700).

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

7644 is a wasteful number, since it uses less digits than its factorization.

7644 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 34 (or 25 counting only the distinct ones).

The product of its digits is 672, while the sum is 21.

The square root of 7644 is about 87.4299719776. The cubic root of 7644 is about 19.6988206497.

It can be divided in two parts, 76 and 44, that added together give a triangular number (120 = T₁₅).

The spelling of 7644 in words is "seven thousand, six hundred forty-four".