1785 has 16 divisors (see below), whose sum is σ = 3456. Its totient is φ = 768.

The previous prime is 1783. The next prime is 1787. The reversal of 1785 is 5871.

1785 = T₁₉ + T₂₀ + ... + T₂₅.

1785 = 1² + 2² + ... + 17².

It is a happy number.

1785 is nontrivially palindromic in base 4.

It is an interprime number because it is at equal distance from previous prime (1783) and next prime (1787).

It is not a de Polignac number, because 1785 - 2¹ = 1783 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a Curzon number.

It is a nialpdrome in base 13.

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 polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 97 + ... + 113.

It is an arithmetic number, because the mean of its divisors is an integer number (216).

2¹⁷⁸⁵ is an apocalyptic number.

1785 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

1785 is a deficient number, since it is larger than the sum of its proper divisors (1671).

1785 is a wasteful number, since it uses less digits than its factorization.

1785 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32.

The product of its digits is 280, while the sum is 21.

The square root of 1785 is about 42.2492603486. The cubic root of 1785 is about 12.1305196819.

Subtracting from 1785 its sum of digits (21), we obtain a square (1764 = 42²).

The spelling of 1785 in words is "one thousand, seven hundred eighty-five".