821772000 has 384 divisors, whose sum is σ = 3421716480. Its totient is φ = 187660800.

The previous prime is 821771981. The next prime is 821772041. The reversal of 821772000 is 277128.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 755457 + ... + 756543.

It is an arithmetic number, because the mean of its divisors is an integer number (8910720).

Almost surely, 2^821772000 is an apocalyptic number.

821772000 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 821772000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1710858240).

821772000 is an abundant number, since it is smaller than the sum of its proper divisors (2599944480).

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

821772000 is a wasteful number, since it uses less digits than its factorization.

821772000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1128 (or 1104 counting only the distinct ones).

The product of its (nonzero) digits is 1568, while the sum is 27.

The square root of 821772000 is about 28666.5658912957. The cubic root of 821772000 is about 936.6638945445.

The spelling of 821772000 in words is "eight hundred twenty-one million, seven hundred seventy-two thousand".