464745600 has 480 divisors, whose sum is σ = 1882401840. Its totient is φ = 111974400.

The previous prime is 464745599. The next prime is 464745607. The reversal of 464745600 is 6547464.

464745600 is a `hidden beast` number, since 4 + 6 + 4 + 7 + 45 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (464745607) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 2851119 + ... + 2851281.

Almost surely, 2^464745600 is an apocalyptic number.

464745600 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 464745600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (941200920).

464745600 is an abundant number, since it is smaller than the sum of its proper divisors (1417656240).

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

464745600 is a wasteful number, since it uses less digits than its factorization.

464745600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 210 (or 184 counting only the distinct ones).

The product of its (nonzero) digits is 80640, while the sum is 36.

The square root of 464745600 is about 21557.9590870750. The cubic root of 464745600 is about 774.5897794330.

The spelling of 464745600 in words is "four hundred sixty-four million, seven hundred forty-five thousand, six hundred".