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75768 = 23371141
BaseRepresentation
bin10010011111111000
310211221020
4102133320
54411033
61342440
7433620
oct223770
9124836
1075768
1151a20
1237a20
1328644
141d880
15176b3
hex127f8

75768 has 64 divisors (see below), whose sum is σ = 241920. Its totient is φ = 19200.

The previous prime is 75767. The next prime is 75773. The reversal of 75768 is 86757.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (75767) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1828 + ... + 1868.

It is an arithmetic number, because the mean of its divisors is an integer number (3780).

275768 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (120960).

75768 is an abundant number, since it is smaller than the sum of its proper divisors (166152).

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

75768 is a wasteful number, since it uses less digits than its factorization.

75768 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 68 (or 64 counting only the distinct ones).

The product of its digits is 11760, while the sum is 33.

The square root of 75768 is about 275.2598772070. The cubic root of 75768 is about 42.3150905477.

It can be divided in two parts, 75 and 768, that multiplied together give a square (57600 = 2402).

The spelling of 75768 in words is "seventy-five thousand, seven hundred sixty-eight".

Divisors: 1 2 3 4 6 7 8 11 12 14 21 22 24 28 33 41 42 44 56 66 77 82 84 88 123 132 154 164 168 231 246 264 287 308 328 451 462 492 574 616 861 902 924 984 1148 1353 1722 1804 1848 2296 2706 3157 3444 3608 5412 6314 6888 9471 10824 12628 18942 25256 37884 75768