85629200 has 90 divisors (see below), whose sum is σ = 217487754. Its totient is φ = 32394240.

The previous prime is 85629169. The next prime is 85629209. The reversal of 85629200 is 292658.

It can be written as a sum of positive squares in 3 ways, for example, as 7907344 + 77721856 = 2812^2 + 8816^2 .

It is not an unprimeable number, because it can be changed into a prime (85629209) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 144104 + ... + 144696.

Almost surely, 2^85629200 is an apocalyptic number.

85629200 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 85629200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108743877).

85629200 is an abundant number, since it is smaller than the sum of its proper divisors (131858554).

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

85629200 is a wasteful number, since it uses less digits than its factorization.

85629200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 649 (or 619 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 32.

The square root of 85629200 is about 9253.6047030333. The cubic root of 85629200 is about 440.7651974108.

The spelling of 85629200 in words is "eighty-five million, six hundred twenty-nine thousand, two hundred".