75420800 has 288 divisors, whose sum is σ = 239711220. Its totient is φ = 23224320.

The previous prime is 75420781. The next prime is 75420803. The reversal of 75420800 is 802457.

It can be written as a sum of positive squares in 6 ways, for example, as 29506624 + 45914176 = 5432^2 + 6776^2 .

It is a Harshad number since it is a multiple of its sum of digits (26).

It is a self number, because there is not a number n which added to its sum of digits gives 75420800.

It is not an unprimeable number, because it can be changed into a prime (75420803) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2038382 + ... + 2038418.

Almost surely, 2^75420800 is an apocalyptic number.

75420800 is a gapful number since it is divisible by the number (70) 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 75420800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119855610).

75420800 is an abundant number, since it is smaller than the sum of its proper divisors (164290420).

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

75420800 is a wasteful number, since it uses less digits than its factorization.

75420800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2240, while the sum is 26.

The square root of 75420800 is about 8684.5149547917. The cubic root of 75420800 is about 422.5035654380.

75420800 divided by its product of nonzero digits (2240) gives a triangular number (33670 = T₂₅₉).

It can be divided in two parts, 7 and 5420800, that multiplied together give a square (37945600 = 6160²).

The spelling of 75420800 in words is "seventy-five million, four hundred twenty thousand, eight hundred".