7838400 has 168 divisors, whose sum is σ = 27212544. Its totient is φ = 1971200.

The previous prime is 7838387. The next prime is 7838407. The reversal of 7838400 is 48387.

7838400 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×7838400² = 122881029120000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7838407) 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, 110365 + ... + 110435.

Almost surely, 2^7838400 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 7838400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13606272).

7838400 is an abundant number, since it is smaller than the sum of its proper divisors (19374144).

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

7838400 is a wasteful number, since it uses less digits than its factorization.

7838400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 119 (or 104 counting only the distinct ones).

The product of its (nonzero) digits is 5376, while the sum is 30.

The square root of 7838400 is about 2799.7142711355. The cubic root of 7838400 is about 198.6441626287.

The spelling of 7838400 in words is "seven million, eight hundred thirty-eight thousand, four hundred".