821348640 has 384 divisors, whose sum is σ = 3325432320. Its totient is φ = 185462784.

The previous prime is 821348639. The next prime is 821348657. The reversal of 821348640 is 46843128.

821348640 is a `hidden beast` number, since 8 + 2 + 1 + 3 + 4 + 8 + 640 = 666.

It is a super-2 number, since 2×821348640² = 1349227176859699200, which contains 22 as substring.

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

It is a junction number, because it is equal to n+sod(n) for n = 821348595 and 821348604.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 4747594 + ... + 4747766.

It is an arithmetic number, because the mean of its divisors is an integer number (8659980).

Almost surely, 2^821348640 is an apocalyptic number.

821348640 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 821348640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1662716160).

821348640 is an abundant number, since it is smaller than the sum of its proper divisors (2504083680).

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

821348640 is a wasteful number, since it uses less digits than its factorization.

821348640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 361 (or 347 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 821348640 is about 28659.1807279971. The cubic root of 821348640 is about 936.5030169356.

The spelling of 821348640 in words is "eight hundred twenty-one million, three hundred forty-eight thousand, six hundred forty".