30720 has 48 divisors (see below), whose sum is σ = 98280. Its totient is φ = 8192.

The previous prime is 30713. The next prime is 30727. The reversal of 30720 is 2703.

It is a Jordan-Polya number, since it can be written as 5! ⋅ (2!)^{8}.

30720 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (30713) and next prime (30727).

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (12).

30720 is strictly pandigital in base 6.

It is a nialpdrome in base 2 and base 8.

It is a zygodrome in base 2.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 30696 and 30705.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 40 × 24 × 32.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (30727) by changing a digit.

30720 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 30720 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, 6142 + ... + 6146.

2^{30720} is an apocalyptic number.

30720 is a gapful number since it is divisible by the number (30) 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 30720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (49140).

30720 is an abundant number, since it is smaller than the sum of its proper divisors (67560).

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

30720 is an equidigital number, since it uses as much as digits as its factorization.

30720 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 42, while the sum is 12.

The square root of 30720 is about 175.2712184017. The cubic root of 30720 is about 31.3189411294.

The spelling of 30720 in words is "thirty thousand, seven hundred twenty".

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 1024 1280 1536 1920 2048 2560 3072 3840 5120 6144 7680 10240 15360 30720

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