85377600 has 567 divisors, whose sum is σ = 388003161. Its totient is φ = 17740800.

The previous prime is 85377577. The next prime is 85377601. The reversal of 85377600 is 677358.

85377600 = T₂₁₁ + T₂₁₂ + ... + T₈₀₄.

The square root of 85377600 is 9240.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 30735936 + 54641664 = 5544^2 + 7392^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (85377601) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 7761595 + ... + 7761605.

Almost surely, 2^85377600 is an apocalyptic number.

85377600 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

85377600 is the 9240-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85377600

85377600 is an abundant number, since it is smaller than the sum of its proper divisors (302625561).

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

85377600 is a wasteful number, since it uses less digits than its factorization.

85377600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 64 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 35280, while the sum is 36.

The cubic root of 85377600 is about 440.3330811264. Note that the first 3 decimals are identical.

Multiplying 85377600 by its sum of digits (36), we get a square (3073593600 = 55440²).

85377600 divided by its sum of digits (36) gives a square (2371600 = 1540²).

The spelling of 85377600 in words is "eighty-five million, three hundred seventy-seven thousand, six hundred".