84272400 has 315 divisors, whose sum is σ = 322464511. Its totient is φ = 21150720.

The previous prime is 84272393. The next prime is 84272401. The reversal of 84272400 is 427248.

84272400 = 1³ + 2³ + ... + 135³.

The square root of 84272400 is 9180.

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

It can be written as a sum of positive squares in 4 ways, for example, as 1971216 + 82301184 = 1404^2 + 9072^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (84272401) by changing a digit.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 4957192 + ... + 4957208.

Almost surely, 2^84272400 is an apocalyptic number.

84272400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

84272400 is the 9180-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 84272400

84272400 is an abundant number, since it is smaller than the sum of its proper divisors (238192111).

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

84272400 is a wasteful number, since it uses less digits than its factorization.

84272400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 70 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The cubic root of 84272400 is about 438.4248083445.

Adding to 84272400 its reverse (427248), we get a palindrome (84699648).

It can be divided in two parts, 84 and 272400, that added together give a square (272484 = 522²).

The spelling of 84272400 in words is "eighty-four million, two hundred seventy-two thousand, four hundred".