826400 has 36 divisors (see below), whose sum is σ = 2019402. Its totient is φ = 330240.

The previous prime is 826393. The next prime is 826403. The reversal of 826400 is 4628.

It can be written as a sum of positive squares in 3 ways, for example, as 781456 + 44944 = 884^2 + 212^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 826400.

It is not an unprimeable number, because it can be changed into a prime (826403) by changing a digit.

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, 284 + ... + 1316.

2⁸²⁶⁴⁰⁰ is an apocalyptic number.

826400 is a gapful number since it is divisible by the number (80) 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 826400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1009701).

826400 is an abundant number, since it is smaller than the sum of its proper divisors (1193002).

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

826400 is a wasteful number, since it uses less digits than its factorization.

826400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1053 (or 1040 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 20.

The square root of 826400 is about 909.0654541891. The cubic root of 826400 is about 93.8418950789.

It can be divided in two parts, 82 and 6400, that multiplied together give a triangular number (524800 = T₁₀₂₄).

The spelling of 826400 in words is "eight hundred twenty-six thousand, four hundred".