464951827200 has 1458 divisors, whose sum is σ = 1936138915116. Its totient is φ = 97960181760.

The previous prime is 464951827187. The next prime is 464951827217. The reversal of 464951827200 is 2728159464.

It is a super-3 number, since 3×464951827200³ (a number of 36 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 464951827200.

It is an unprimeable number.

It is a polite number, since it can be written in 161 ways as a sum of consecutive naturals, for example, 12566265582 + ... + 12566265618.

Almost surely, 2^464951827200 is an apocalyptic number.

464951827200 is a gapful number since it is divisible by the number (40) 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 464951827200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (968069457558).

464951827200 is an abundant number, since it is smaller than the sum of its proper divisors (1471187087916).

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

464951827200 is a wasteful number, since it uses less digits than its factorization.

464951827200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 155 (or 73 counting only the distinct ones).

The product of its (nonzero) digits is 967680, while the sum is 48.

Multiplying 464951827200 by its sum of digits (48), we get a square (22317687705600 = 4724160²).

464951827200 divided by its sum of digits (48) gives a square (9686496400 = 98420²).

The spelling of 464951827200 in words is "four hundred sixty-four billion, nine hundred fifty-one million, eight hundred twenty-seven thousand, two hundred".