46008817680400 has 135 divisors (see below), whose sum is σ = 111095997202533. Its totient is φ = 18310790169600.

The previous prime is 46008817680349. The next prime is 46008817680401. The reversal of 46008817680400 is 408671880064.

The square root of 46008817680400 is 6782980.

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

It can be written as a sum of positive squares in 13 ways, for example, as 9779204717584 + 36229612962816 = 3127172^2 + 6019104^2 .

It is a super-2 number, since 2×46008817680400² (a number of 28 digits) contains 22 as substring.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (46008817680401) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 31066047660 + ... + 31066049140.

Almost surely, 2^{46008817680400} is an apocalyptic number.

46008817680400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

46008817680400 is the 6782980-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 46008817680400

46008817680400 is an abundant number, since it is smaller than the sum of its proper divisors (65087179522133).

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

46008817680400 is an frugal number, since it uses more digits than its factorization.

46008817680400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3438 (or 1717 counting only the distinct ones).

The product of its (nonzero) digits is 2064384, while the sum is 52.

The spelling of 46008817680400 in words is "forty-six trillion, eight billion, eight hundred seventeen million, six hundred eighty thousand, four hundred".