820448640 has 384 divisors, whose sum is σ = 3230772480. Its totient is φ = 189911040.

The previous prime is 820448623. The next prime is 820448641. The reversal of 820448640 is 46844028.

820448640 is a `hidden beast` number, since 8 + 2 + 0 + 4 + 4 + 8 + 640 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-3 number, since 3×820448640³ (a number of 28 digits) contains 333 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 = 820448595 and 820448604.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820448641) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1456999 + ... + 1457561.

It is an arithmetic number, because the mean of its divisors is an integer number (8413470).

Almost surely, 2^820448640 is an apocalyptic number.

820448640 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 820448640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1615386240).

820448640 is an abundant number, since it is smaller than the sum of its proper divisors (2410323840).

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

820448640 is a wasteful number, since it uses less digits than its factorization.

820448640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 622 (or 607 counting only the distinct ones).

The product of its (nonzero) digits is 49152, while the sum is 36.

The square root of 820448640 is about 28643.4746495602. The cubic root of 820448640 is about 936.1608314469.

The spelling of 820448640 in words is "eight hundred twenty million, four hundred forty-eight thousand, six hundred forty".