1780 has 12 divisors (see below), whose sum is σ = 3780. Its totient is φ = 704.

The previous prime is 1777. The next prime is 1783. The reversal of 1780 is 871.

1780 = 3² + 4² + ... + 17².

It is an interprime number because it is at equal distance from previous prime (1777) and next prime (1783).

It can be written as a sum of positive squares in 2 ways, for example, as 484 + 1296 = 22^2 + 36^2 .

It is a plaindrome in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1783) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 25 + ... + 64.

It is an arithmetic number, because the mean of its divisors is an integer number (315).

1780 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

1780 is an abundant number, since it is smaller than the sum of its proper divisors (2000).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1890).

1780 is a wasteful number, since it uses less digits than its factorization.

1780 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 56, while the sum is 16.

The square root of 1780 is about 42.1900462195. The cubic root of 1780 is about 12.1191827411.

Subtracting from 1780 its sum of digits (16), we obtain a square (1764 = 42²).

Subtracting from 1780 its reverse (871), we obtain a palindrome (909).

The spelling of 1780 in words is "one thousand, seven hundred eighty".