820689408 has 400 divisors, whose sum is σ = 3065857344. Its totient is φ = 212336640.

The previous prime is 820689391. The next prime is 820689409. The reversal of 820689408 is 804986028.

It is a happy number.

It is a super-2 number, since 2×820689408² = 1347062208806780928, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (820689409) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 3193216 + ... + 3193472.

Almost surely, 2^820689408 is an apocalyptic number.

820689408 is a gapful number since it is divisible by the number (88) 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 820689408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1532928672).

820689408 is an abundant number, since it is smaller than the sum of its proper divisors (2245167936).

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

820689408 is a wasteful number, since it uses less digits than its factorization.

820689408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 305 (or 280 counting only the distinct ones).

The product of its (nonzero) digits is 221184, while the sum is 45.

The square root of 820689408 is about 28647.6771833250. The cubic root of 820689408 is about 936.2523974168.

The spelling of 820689408 in words is "eight hundred twenty million, six hundred eighty-nine thousand, four hundred eight".