456121600 has 324 divisors, whose sum is σ = 1348385920. Its totient is φ = 152064000.

The previous prime is 456121591. The next prime is 456121609. The reversal of 456121600 is 6121654.

It is an interprime number because it is at equal distance from previous prime (456121591) and next prime (456121609).

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456121609) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 14713585 + ... + 14713615.

Almost surely, 2^456121600 is an apocalyptic number.

456121600 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 456121600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (674192960).

456121600 is an abundant number, since it is smaller than the sum of its proper divisors (892264320).

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

456121600 is a wasteful number, since it uses less digits than its factorization.

456121600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 68 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 25.

The square root of 456121600 is about 21357.0035351404. The cubic root of 456121600 is about 769.7686379726.

The spelling of 456121600 in words is "four hundred fifty-six million, one hundred twenty-one thousand, six hundred".