75342400 has 189 divisors, whose sum is σ = 222838137. Its totient is φ = 24998400.

The previous prime is 75342383. The next prime is 75342401. The reversal of 75342400 is 424357.

The square root of 75342400 is 8680.

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., 27123264 + 48219136 = 5208^2 + 6944^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is not an unprimeable number, because it can be changed into a prime (75342401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 2430385 + ... + 2430415.

Almost surely, 2^75342400 is an apocalyptic number.

75342400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

75342400 is the 8680-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75342400

75342400 is an abundant number, since it is smaller than the sum of its proper divisors (147495737).

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

75342400 is a wasteful number, since it uses less digits than its factorization.

75342400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 45 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 25.

The cubic root of 75342400 is about 422.3571170500.

Multiplying 75342400 by its sum of digits (25), we get a square (1883560000 = 43400²).

75342400 divided by its sum of digits (25) gives a square (3013696 = 1736²).

Adding to 75342400 its reverse (424357), we get a palindrome (75766757).

The spelling of 75342400 in words is "seventy-five million, three hundred forty-two thousand, four hundred".