61440 has 52 divisors (see below), whose sum is σ = 196584. Its totient is φ = 16384.

The previous prime is 61417. The next prime is 61441. The reversal of 61440 is 4416.

It is a Jordan-Polya number, since it can be written as 5! ⋅ (2!)^{9}.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 2, base 4 and base 16.

It is a zygodrome in base 2 and base 4.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (61441) by changing a digit.

61440 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

In principle, a polygon with 61440 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 12286 + ... + 12290.

61440 is a Friedman number, since it can be written as 60*4^(4+1), using all its digits and the basic arithmetic operations.

2^{61440} is an apocalyptic number.

61440 is a gapful number since it is divisible by the number (60) 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 61440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (98292).

61440 is an abundant number, since it is smaller than the sum of its proper divisors (135144).

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

61440 is an equidigital number, since it uses as much as digits as its factorization.

61440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 61440 is about 247.8709341573. The cubic root of 61440 is about 39.4593931893.

Subtracting from 61440 its sum of digits (15), we obtain a triangular number (61425 = T_{350}).

Multiplying 61440 by its sum of digits (15), we get a square (921600 = 960^{2}).

61440 divided by its sum of digits (15) gives a 12-th power (4096 = 2^{12}).

Adding to 61440 its reverse (4416), we get a palindrome (65856).

The spelling of 61440 in words is "sixty-one thousand, four hundred forty".

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 64 80 96 120 128 160 192 240 256 320 384 480 512 640 768 960 1024 1280 1536 1920 2048 2560 3072 3840 4096 5120 6144 7680 10240 12288 15360 20480 30720 61440

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