7830 has 32 divisors (see below), whose sum is σ = 21600. Its totient is φ = 2016.

The previous prime is 7829. The next prime is 7841. The reversal of 7830 is 387.

It is a super-2 number, since 2×7830² = 122617800, which contains 22 as substring.

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

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

7830 is an undulating number in base 12.

It is a Curzon number.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 256 + ... + 284.

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

2⁷⁸³⁰ is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7830, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10800).

7830 is an abundant number, since it is smaller than the sum of its proper divisors (13770).

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

7830 is a wasteful number, since it uses less digits than its factorization.

7830 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 45 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 18.

The square root of 7830 is about 88.4872872225. The cubic root of 7830 is about 19.8573178441.

7830 divided by its sum of digits (18) gives a triangular number (435 = T₂₉).

The spelling of 7830 in words is "seven thousand, eight hundred thirty".