448364800 has 216 divisors, whose sum is σ = 1269434376. Its totient is φ = 155320320.

The previous prime is 448364797. The next prime is 448364803. The reversal of 448364800 is 8463844.

It is an interprime number because it is at equal distance from previous prime (448364797) and next prime (448364803).

It can be written as a sum of positive squares in 12 ways, for example, as 255488256 + 192876544 = 15984^2 + 13888^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 448364800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (448364803) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1414242 + ... + 1414558.

It is an arithmetic number, because the mean of its divisors is an integer number (5877011).

Almost surely, 2^448364800 is an apocalyptic number.

448364800 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 448364800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (634717188).

448364800 is an abundant number, since it is smaller than the sum of its proper divisors (821069576).

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

448364800 is a wasteful number, since it uses less digits than its factorization.

448364800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 373 (or 354 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 37.

The square root of 448364800 is about 21174.6263249201. The cubic root of 448364800 is about 765.3801064328.

The spelling of 448364800 in words is "four hundred forty-eight million, three hundred sixty-four thousand, eight hundred".