7632 has 30 divisors (see below), whose sum is σ = 21762. Its totient is φ = 2496.

The previous prime is 7621. The next prime is 7639. The reversal of 7632 is 2367.

It can be written as a sum of positive squares in only one way, i.e., 7056 + 576 = 84^2 + 24^2 .

It is a super-3 number, since 3×7632³ = 1333633019904, which contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a d-powerful number, because it can be written as 7³ + 3⁸ + 6³ + 2⁹ .

It is an alternating number because its digits alternate between odd and even.

It is a nialpdrome in base 6 and base 10.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 7632.

It is not an unprimeable number, because it can be changed into a prime (7639) by changing a digit.

7632 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 5 ways as a sum of consecutive naturals, for example, 118 + ... + 170.

2⁷⁶³² is an apocalyptic number.

7632 is a gapful number since it is divisible by the number (72) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7632, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10881).

7632 is an abundant number, since it is smaller than the sum of its proper divisors (14130).

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

7632 is a wasteful number, since it uses less digits than its factorization.

7632 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 67 (or 58 counting only the distinct ones).

The product of its digits is 252, while the sum is 18.

The square root of 7632 is about 87.3613186714. The cubic root of 7632 is about 19.6885071291.

7632 divided by its sum of digits (18) gives a palindrome (424).

Adding to 7632 its reverse (2367), we get a palindrome (9999).

The spelling of 7632 in words is "seven thousand, six hundred thirty-two".