84142800 has 450 divisors, whose sum is σ = 357912918. Its totient is φ = 18869760.

The previous prime is 84142777. The next prime is 84142801. The reversal of 84142800 is 824148.

It can be written as a sum of positive squares in 3 ways, for example, as 10732176 + 73410624 = 3276^2 + 8568^2 .

It is a tau number, because it is divible by the number of its divisors (450).

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 (84142801) by changing a digit.

It is a polite number, since it can be written in 89 ways as a sum of consecutive naturals, for example, 1587574 + ... + 1587626.

Almost surely, 2^84142800 is an apocalyptic number.

84142800 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 84142800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178956459).

84142800 is an abundant number, since it is smaller than the sum of its proper divisors (273770118).

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

84142800 is a wasteful number, since it uses less digits than its factorization.

84142800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 97 (or 70 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 27.

The square root of 84142800 is about 9172.9384604935. The cubic root of 84142800 is about 438.1999462415.

Adding to 84142800 its reverse (824148), we get a palindrome (84966948).

It can be divided in two parts, 84 and 142800, that added together give a square (142884 = 378²).

The spelling of 84142800 in words is "eighty-four million, one hundred forty-two thousand, eight hundred".