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82824 = 23371729
BaseRepresentation
bin10100001110001000
311012121120
4110032020
510122244
61435240
7463320
oct241610
9135546
1082824
1157255
123bb20
132b911
1422280
1519819
hex14388

82824 has 64 divisors (see below), whose sum is σ = 259200. Its totient is φ = 21504.

The previous prime is 82813. The next prime is 82837. The reversal of 82824 is 42828.

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

It is a nude number because it is divisible by every one of its digits.

It is a junction number, because it is equal to n+sod(n) for n = 82794 and 82803.

It is an unprimeable number.

82824 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2842 + ... + 2870.

It is an arithmetic number, because the mean of its divisors is an integer number (4050).

282824 is an apocalyptic number.

82824 is a gapful number since it is divisible by the number (84) 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 82824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129600).

82824 is an abundant number, since it is smaller than the sum of its proper divisors (176376).

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

82824 is a wasteful number, since it uses less digits than its factorization.

82824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 62 (or 58 counting only the distinct ones).

The product of its digits is 1024, while the sum is 24.

The square root of 82824 is about 287.7915912601. The cubic root of 82824 is about 43.5898525890.

The spelling of 82824 in words is "eighty-two thousand, eight hundred twenty-four".

Divisors: 1 2 3 4 6 7 8 12 14 17 21 24 28 29 34 42 51 56 58 68 84 87 102 116 119 136 168 174 203 204 232 238 348 357 406 408 476 493 609 696 714 812 952 986 1218 1428 1479 1624 1972 2436 2856 2958 3451 3944 4872 5916 6902 10353 11832 13804 20706 27608 41412 82824