131712 has 64 divisors (see below), whose sum is σ = 408000. Its totient is φ = 37632.

The previous prime is 131711. The next prime is 131713. The reversal of 131712 is 217131.

Multipling 131712 by its product of digits (42), we get a square (5531904 = 2352^{2}).

131712 divided by its product of digits (42) gives a square (3136 = 56^{2}).

Adding to 131712 its reverse (217131), we get a palindrome (348843).

It can be divided in two parts, 1 and 31712, that added together give a palindrome (31713).

It is an interprime number because it is at equal distance from previous prime (131711) and next prime (131713).

It is a tau number, because it is divible by the number of its divisors (64).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 131691 and 131700.

It is not an unprimeable number, because it can be changed into a prime (131711) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 18813 + ... + 18819.

It is an arithmetic number, because the mean of its divisors is an integer number (6375).

2^{131712} is an apocalyptic number.

131712 is a gapful number since it is divisible by the number (12) 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 131712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (204000).

131712 is an abundant number, since it is smaller than the sum of its proper divisors (276288).

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

131712 is an frugal number, since it uses more digits than its factorization.

131712 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 12 counting only the distinct ones).

The product of its digits is 42, while the sum is 15.

The square root of 131712 is about 362.9214791108. The cubic root of 131712 is about 50.8793765993.

The spelling of 131712 in words is "one hundred thirty-one thousand, seven hundred twelve".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 49 56 64 84 96 98 112 128 147 168 192 196 224 294 336 343 384 392 448 588 672 686 784 896 1029 1176 1344 1372 1568 2058 2352 2688 2744 3136 4116 4704 5488 6272 8232 9408 10976 16464 18816 21952 32928 43904 65856 131712

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