96768 has 80 divisors (see below), whose sum is σ = 327360. Its totient is φ = 27648.

The previous prime is 96763. The next prime is 96769. The reversal of 96768 is 86769.

Subtracting from 96768 its reverse (86769), we obtain a palindrome (9999).

It can be divided in two parts, 967 and 68, that multiplied together give a palindrome (65756).

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

It is a nude number because it is divisible by every one of its digits.

Its product of digits (18144) is a multiple of the sum of its prime divisors (12).

It is not an unprimeable number, because it can be changed into a prime (96763) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 13821 + ... + 13827.

It is an arithmetic number, because the mean of its divisors is an integer number (4092).

2^{96768} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 96768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163680).

96768 is an abundant number, since it is smaller than the sum of its proper divisors (230592).

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

96768 is an equidigital number, since it uses as much as digits as its factorization.

96768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 34 (or 12 counting only the distinct ones).

The product of its digits is 18144, while the sum is 36.

The square root of 96768 is about 311.0755535236. The cubic root of 96768 is about 45.9103483865.

The spelling of 96768 in words is "ninety-six thousand, seven hundred sixty-eight".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 64 72 84 96 108 112 126 128 144 168 189 192 216 224 252 256 288 336 378 384 432 448 504 512 576 672 756 768 864 896 1008 1152 1344 1512 1536 1728 1792 2016 2304 2688 3024 3456 3584 4032 4608 5376 6048 6912 8064 10752 12096 13824 16128 24192 32256 48384 96768

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