9967688640 has 672 divisors, whose sum is σ = 42856684416. Its totient is φ = 2070282240.

The previous prime is 9967688639. The next prime is 9967688671. The reversal of 9967688640 is 468867699.

It is a tau number, because it is divible by the number of its divisors (672).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 19131580 + ... + 19132100.

It is an arithmetic number, because the mean of its divisors is an integer number (63774828).

Almost surely, 2^9967688640 is an apocalyptic number.

9967688640 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 9967688640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21428342208).

9967688640 is an abundant number, since it is smaller than the sum of its proper divisors (32888995776).

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

9967688640 is a wasteful number, since it uses less digits than its factorization.

9967688640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 637 (or 624 counting only the distinct ones).

The product of its (nonzero) digits is 31352832, while the sum is 63.

The square root of 9967688640 is about 99838.3124857387. The cubic root of 9967688640 is about 2152.1117625054. Note that the first 3 decimals are identical.

The spelling of 9967688640 in words is "nine billion, nine hundred sixty-seven million, six hundred eighty-eight thousand, six hundred forty".