45676800 has 324 divisors, whose sum is σ = 178749844. Its totient is φ = 11059200.

The previous prime is 45676789. The next prime is 45676801. The reversal of 45676800 is 867654.

It is a happy number.

It can be written as a sum of positive squares in 6 ways, for example, as 16257024 + 29419776 = 4032^2 + 5424^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45676801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 748770 + ... + 748830.

Almost surely, 2^45676800 is an apocalyptic number.

45676800 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 45676800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89374922).

45676800 is an abundant number, since it is smaller than the sum of its proper divisors (133073044).

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

45676800 is a wasteful number, since it uses less digits than its factorization.

45676800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 106 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 40320, while the sum is 36.

The square root of 45676800 is about 6758.4613633578. The cubic root of 45676800 is about 357.4636538595.

The spelling of 45676800 in words is "forty-five million, six hundred seventy-six thousand, eight hundred".