10752 has 40 divisors (see below), whose sum is σ = 32736. Its totient is φ = 3072.

The previous prime is 10739. The next prime is 10753. The reversal of 10752 is 25701.

It is a happy number.

It is a plaindrome in base 9.

It is a nialpdrome in base 4.

It is a zygodrome in base 4.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 10752.

It is not an unprimeable number, because it can be changed into a prime (10753) by changing a digit.

10752 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 (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1533 + ... + 1539.

2^{10752} is an apocalyptic number.

10752 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 10752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16368).

10752 is an abundant number, since it is smaller than the sum of its proper divisors (21984).

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

10752 is an frugal number, since it uses more digits than its factorization.

10752 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 70, while the sum is 15.

The square root of 10752 is about 103.6918511745. The cubic root of 10752 is about 22.0713934110.

The spelling of 10752 in words is "ten thousand, seven hundred fifty-two".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 64 84 96 112 128 168 192 224 256 336 384 448 512 672 768 896 1344 1536 1792 2688 3584 5376 10752

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