1920 has 32 divisors (see below), whose sum is σ = 6120. Its totient is φ = 512.

The previous prime is 1913. The next prime is 1931. The reversal of 1920 is 291.

Added to its reverse (291) it gives a triangular number (2211 = T_{66}).

1920 = T_{16} + T_{17} + ... +
T_{24}.

It is a happy number.

It is a Jordan-Polya number, since it can be written as 5! ⋅ (2!)^{4}.

It is a tau number, because it is divible by the number of its divisors (32).

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

It is a nialpdrome in base 2 and base 15.

It is a zygodrome in base 2.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 1896 and 1905.

It is a congruent number.

It is an unprimeable number.

1920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 1920 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, 382 + ... + 386.

1920 is a gapful number since it is divisible by the number (10) 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 1920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (3060).

1920 is an abundant number, since it is smaller than the sum of its proper divisors (4200).

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

1920 is an equidigital number, since it uses as much as digits as its factorization.

1920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 22 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 18, while the sum is 12.

The square root of 1920 is about 43.8178046004. The cubic root of 1920 is about 12.4289300238.

Adding to 1920 its reverse (291), we get a triangular number (2211 = T_{66}).

The spelling of 1920 in words is "one thousand, nine hundred twenty".

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

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