75264 has 60 divisors (see below), whose sum is σ = 233244. Its totient is φ = 21504.

The previous prime is 75253. The next prime is 75269. The reversal of 75264 is 46257.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

Its product of digits (1680) is a multiple of the sum of its prime divisors (12).

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 75264.

It is not an unprimeable number, because it can be changed into a prime (75269) 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, 10749 + ... + 10755.

2^{75264} is an apocalyptic number.

75264 is the 147-th nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (116622).

75264 is an abundant number, since it is smaller than the sum of its proper divisors (157980).

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

75264 is an equidigital number, since it uses as much as digits as its factorization.

75264 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 12 counting only the distinct ones).

The product of its digits is 1680, while the sum is 24.

The square root of 75264 is about 274.3428511917. The cubic root of 75264 is about 42.2210567032.

Multiplying 75264 by its sum of digits (24), we get a square (1806336 = 1344^{2}).

75264 divided by its sum of digits (24) gives a square (3136 = 56^{2}).

The spelling of 75264 in words is "seventy-five thousand, two hundred sixty-four".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 49 56 64 84 96 98 112 128 147 168 192 196 224 256 294 336 384 392 448 512 588 672 768 784 896 1176 1344 1536 1568 1792 2352 2688 3136 3584 4704 5376 6272 9408 10752 12544 18816 25088 37632 75264

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