827712 has 56 divisors (see below), whose sum is σ = 2438400. Its totient is φ = 275328.

The previous prime is 827699. The next prime is 827719. The reversal of 827712 is 217728.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (827719) by changing a digit.

827712 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1489 + ... + 1967.

2⁸²⁷⁷¹² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 827712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1219200).

827712 is an abundant number, since it is smaller than the sum of its proper divisors (1610688).

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

827712 is a wasteful number, since it uses less digits than its factorization.

827712 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 500 (or 484 counting only the distinct ones).

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

The square root of 827712 is about 909.7867882092. The cubic root of 827712 is about 93.8915302305.

The spelling of 827712 in words is "eight hundred twenty-seven thousand, seven hundred twelve".