3744 has 36 divisors (see below), whose sum is σ = 11466. Its totient is φ = 1152.

The previous prime is 3739. The next prime is 3761. The reversal of 3744 is 4473.

It can be written as a sum of positive squares in only one way, i.e., 3600 + 144 = 60^2 + 12^2 .

It is a tau number, because it is divible by the number of its divisors (36).

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

It is a plaindrome in base 15.

It is a nialpdrome in base 4, base 12 and base 16.

It is a zygodrome in base 12 and base 15.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 3744.

It is an unprimeable number.

3744 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 282 + ... + 294.

2^{3744} is an apocalyptic number.

3744 is the 39-th heptagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 3744, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5733).

3744 is an abundant number, since it is smaller than the sum of its proper divisors (7722).

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

3744 is a wasteful number, since it uses less digits than its factorization.

3744 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 29 (or 18 counting only the distinct ones).

The product of its digits is 336, while the sum is 18.

The square root of 3744 is about 61.1882341631. The cubic root of 3744 is about 15.5278721533.

Subtracting 3744 from its reverse (4473), we obtain a 6-th power (729 = 3^{6}).

It can be divided in two parts, 374 and 4, that added together give a triangular number (378 = T_{27}).

The spelling of 3744 in words is "three thousand, seven hundred forty-four", and thus it is an iban number.

Divisors: 1 2 3 4 6 8 9 12 13 16 18 24 26 32 36 39 48 52 72 78 96 104 117 144 156 208 234 288 312 416 468 624 936 1248 1872 3744

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