42828124262400 has 1053 divisors, whose sum is σ = 163362912409333. Its totient is φ = 10722213888000.

The previous prime is 42828124262387. The next prime is 42828124262423. The reversal of 42828124262400 is 426242182824.

The square root of 42828124262400 is 6544320.

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

42828124262400 is a `hidden beast` number, since 4 + 2 + 8 + 2 + 8 + 12 + 4 + 2 + 624 + 0 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 123049414656 + 42705074847744 = 350784^2 + 6534912^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a Duffinian number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 106803302200 + ... + 106803302600.

Almost surely, 2^{42828124262400} is an apocalyptic number.

42828124262400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

42828124262400 is the 6544320-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 42828124262400

42828124262400 is an abundant number, since it is smaller than the sum of its proper divisors (120534788146933).

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

42828124262400 is an equidigital number, since it uses as much as digits as its factorization.

42828124262400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 876 (or 428 counting only the distinct ones).

The product of its (nonzero) digits is 786432, while the sum is 45.

The spelling of 42828124262400 in words is "forty-two trillion, eight hundred twenty-eight billion, one hundred twenty-four million, two hundred sixty-two thousand, four hundred".