1764 has 27 divisors (see below), whose sum is σ = 5187. Its totient is φ = 504.

The previous prime is 1759. The next prime is 1777. The reversal of 1764 is 4671.

Subtracting from 1764 its product of digits (168), we obtain a triangular number (1596 = T_{56}).

It can be divided in two parts, 17 and 64, that added together give a 4-th power (81 = 3^{4}).

1764 = T_{41} + T_{42}.

The square root of 1764 is 42.

It is a perfect power (a square), and thus also a powerful number.

1764 is an esthetic number in base 4, because in such base its adjacent digits differ by 1.

It is a super-2 number, since 2×1764^{2} = 6223392, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

Its product of digits (168) is a multiple of the sum of its prime divisors (12).

It is a plaindrome in base 8.

It is a nialpdrome in base 7 and base 14.

It is a zygodrome in base 8.

It is an unprimeable number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 249 + ... + 255.

1764 is a gapful number since it is divisible by the number (14) formed by its first and last digit.

1764 is the 42-nd square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1764

1764 is an abundant number, since it is smaller than the sum of its proper divisors (3423).

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

1764 is a wasteful number, since it uses less digits than its factorization.

1764 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 24 (or 12 counting only the distinct ones).

The product of its digits is 168, while the sum is 18.

The cubic root of 1764 is about 12.0827612360.

The spelling of 1764 in words is "one thousand, seven hundred sixty-four".

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