1749 has 8 divisors (see below), whose sum is σ = 2592. Its totient is φ = 1040.

The previous prime is 1747. The next prime is 1753. The reversal of 1749 is 9471.

1749 is an esthetic number in base 3, because in such base its adjacent digits differ by 1.

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 1749 - 2¹ = 1747 is a prime.

It is a Curzon number.

1749 is a lucky number.

It is a plaindrome in base 5 and base 14.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1741) 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 7 ways as a sum of consecutive naturals, for example, 7 + ... + 59.

It is an arithmetic number, because the mean of its divisors is an integer number (324).

It is an amenable number.

1749 is a deficient number, since it is larger than the sum of its proper divisors (843).

1749 is a wasteful number, since it uses less digits than its factorization.

1749 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 67.

The product of its digits is 252, while the sum is 21.

The square root of 1749 is about 41.8210473327. The cubic root of 1749 is about 12.0484155099.

Adding to 1749 its sum of digits (21), we get a triangular number (1770 = T₅₉).

Subtracting from 1749 its sum of digits (21), we obtain a cube (1728 = 12³).

It can be divided in two parts, 17 and 49, that added together give a palindrome (66).

The spelling of 1749 in words is "one thousand, seven hundred forty-nine".