9967082400 has 864 divisors, whose sum is σ = 40947379200. Its totient is φ = 2345241600.

The previous prime is 9967082393. The next prime is 9967082417. The reversal of 9967082400 is 42807699.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (864).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 126165561 + ... + 126165639.

It is an arithmetic number, because the mean of its divisors is an integer number (47392800).

Almost surely, 2^9967082400 is an apocalyptic number.

9967082400 is a gapful number since it is divisible by the number (90) 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 9967082400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20473689600).

9967082400 is an abundant number, since it is smaller than the sum of its proper divisors (30980296800).

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

9967082400 is a wasteful number, since it uses less digits than its factorization.

9967082400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 184 (or 159 counting only the distinct ones).

The product of its (nonzero) digits is 217728, while the sum is 45.

The square root of 9967082400 is about 99835.2763305636. The cubic root of 9967082400 is about 2152.0681307691.

The spelling of 9967082400 in words is "nine billion, nine hundred sixty-seven million, eighty-two thousand, four hundred".