7828128 has 144 divisors (see below), whose sum is σ = 27832896. Its totient is φ = 2027520.

The previous prime is 7828123. The next prime is 7828129. The reversal of 7828128 is 8218287.

7828128 is digitally balanced in base 4 and base 8, because in such bases it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×7828128² = 122559175968768, which contains 22 as substring.

It is a Smith number, since the sum of its digits (36) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (36).

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

7828128 is strictly pandigital in base 8.

It is a junction number, because it is equal to n+sod(n) for n = 7828092 and 7828101.

It is not an unprimeable number, because it can be changed into a prime (7828123) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 22000 + ... + 22352.

It is an arithmetic number, because the mean of its divisors is an integer number (193284).

Almost surely, 2^7828128 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 7828128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13916448).

7828128 is an abundant number, since it is smaller than the sum of its proper divisors (20004768).

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

7828128 is a wasteful number, since it uses less digits than its factorization.

7828128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 387 (or 376 counting only the distinct ones).

The product of its digits is 14336, while the sum is 36.

The square root of 7828128 is about 2797.8791968203. The cubic root of 7828128 is about 198.5573521905.

The spelling of 7828128 in words is "seven million, eight hundred twenty-eight thousand, one hundred twenty-eight".