464742400 has 144 divisors (see below), whose sum is σ = 1195821900. Its totient is φ = 178913280.

The previous prime is 464742361. The next prime is 464742401. The reversal of 464742400 is 4247464.

It can be written as a sum of positive squares in 6 ways, for example, as 41370624 + 423371776 = 6432^2 + 20576^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (464742401) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1484644 + ... + 1484956.

Almost surely, 2^464742400 is an apocalyptic number.

464742400 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 464742400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (597910950).

464742400 is an abundant number, since it is smaller than the sum of its proper divisors (731079500).

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

464742400 is a wasteful number, since it uses less digits than its factorization.

464742400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 374 (or 349 counting only the distinct ones).

The product of its (nonzero) digits is 21504, while the sum is 31.

The square root of 464742400 is about 21557.8848684188. The cubic root of 464742400 is about 774.5880016196.

Adding to 464742400 its reverse (4247464), we get a palindrome (468989864).

It can be divided in two parts, 464 and 742400, that multiplied together give a square (344473600 = 18560²).

The spelling of 464742400 in words is "four hundred sixty-four million, seven hundred forty-two thousand, four hundred".