7680 has 40 divisors (see below), whose sum is σ = 24552. Its totient is φ = 2048.

The previous prime is 7673. The next prime is 7681. The reversal of 7680 is 867.

It is a Jordan-Polya number, since it can be written as 5! ⋅ (2!)^{6}.

It is a tau number, because it is divible by the number of its divisors (40).

It is a nialpdrome in base 2 and base 6.

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7681) by changing a digit.

7680 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 7680 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1534 + ... + 1538.

2^{7680} 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 7680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (12276).

7680 is an abundant number, since it is smaller than the sum of its proper divisors (16872).

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

7680 is an equidigital number, since it uses as much as digits as its factorization.

7680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 26 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 21.

The square root of 7680 is about 87.6356092008. The cubic root of 7680 is about 19.7296965946.

The spelling of 7680 in words is "seven thousand, six hundred eighty".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 64 80 96 120 128 160 192 240 256 320 384 480 512 640 768 960 1280 1536 1920 2560 3840 7680

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