1440 has 36 divisors (see below), whose sum is σ = 4914. Its totient is φ = 384.

The previous prime is 1439. The next prime is 1447. The reversal of 1440 is 441.

Adding to 1440 its reverse (441), we get a palindrome (1881).

Subtracting from 1440 its reverse (441), we obtain a palindrome (999).

It can be divided in two parts, 1 and 440, that added together give a square (441 = 21^{2}).

It is a Jordan-Polya number, since it can be written as 6! ⋅ 2!.

It can be written as a sum of positive squares in only one way, i.e., 1296 + 144 = 36^2 + 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 (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 12 and base 15.

It is a zygodrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (1447) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 286 + ... + 290.

1440 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2457).

1440 is an abundant number, since it is smaller than the sum of its proper divisors (3474).

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

1440 is a wasteful number, since it uses less digits than its factorization.

1440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The square root of 1440 is about 37.9473319220. The cubic root of 1440 is about 11.2924323466.

The spelling of 1440 in words is "one thousand, four hundred forty", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 288 360 480 720 1440

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