103680 has 90 divisors (see below), whose sum is σ = 370986. Its totient is φ = 27648.

The previous prime is 103669. The next prime is 103681. The reversal of 103680 is 86301.

Adding to 103680 its reverse (86301), we get a palindrome (189981).

It is a Jordan-Polya number, since it can be written as 6! ⋅ 4! ⋅ 3!.

It can be written as a sum of positive squares in only one way, i.e., 82944 + 20736 = 288^2 + 144^2 .

It is a tau number, because it is divible by the number of its divisors (90).

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

It is a nialpdrome in base 12.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 60 × 36 × 48.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 103680.

It is not an unprimeable number, because it can be changed into a prime (103681) by changing a digit.

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 9 ways as a sum of consecutive naturals, for example, 20734 + ... + 20738.

103680 is a Friedman number, since it can be written as 80*6^(3+1+0), using all its digits and the basic arithmetic operations.

2^{103680} is an apocalyptic number.

103680 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 103680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (185493).

103680 is an abundant number, since it is smaller than the sum of its proper divisors (267306).

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

103680 is an frugal number, since it uses more digits than its factorization.

103680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 33 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 103680 is about 321.9937887600. The cubic root of 103680 is about 46.9784116940.

The spelling of 103680 in words is "one hundred three thousand, six hundred eighty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 81 90 96 108 120 128 135 144 160 162 180 192 216 240 256 270 288 320 324 360 384 405 432 480 540 576 640 648 720 768 810 864 960 1080 1152 1280 1296 1440 1620 1728 1920 2160 2304 2592 2880 3240 3456 3840 4320 5184 5760 6480 6912 8640 10368 11520 12960 17280 20736 25920 34560 51840 103680

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