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214368 = 25371129
BaseRepresentation
bin110100010101100000
3101220001120
4310111200
523324433
64332240
71551660
oct642540
9356046
10214368
11137070
12a4080
137675b
14581a0
15437b3
hex34560

214368 has 96 divisors (see below), whose sum is σ = 725760. Its totient is φ = 53760.

The previous prime is 214363. The next prime is 214373. The reversal of 214368 is 863412.

It can be divided in two parts, 2143 and 68, that added together give a triangular number (2211 = T66).

It is a happy number.

It is a Cunningham number, because it is equal to 4632-1.

It is an interprime number because it is at equal distance from previous prime (214363) and next prime (214373).

It is a tau number, because it is divible by the number of its divisors (96).

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 one of the 548 Lynch-Bell numbers.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (214363) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 7378 + ... + 7406.

It is an arithmetic number, because the mean of its divisors is an integer number (7560).

214368 is a Friedman number, since it can be written as 463^2-1^8, using all its digits and the basic arithmetic operations.

2214368 is an apocalyptic number.

214368 is a gapful number since it is divisible by the number (28) 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 214368, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (362880).

214368 is an abundant number, since it is smaller than the sum of its proper divisors (511392).

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

214368 is a wasteful number, since it uses less digits than its factorization.

214368 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 60 (or 52 counting only the distinct ones).

The product of its digits is 1152, while the sum is 24.

The square root of 214368 is about 462.9989200851. The cubic root of 214368 is about 59.8485067072.

The spelling of 214368 in words is "two hundred fourteen thousand, three hundred sixty-eight".

Divisors: 1 2 3 4 6 7 8 11 12 14 16 21 22 24 28 29 32 33 42 44 48 56 58 66 77 84 87 88 96 112 116 132 154 168 174 176 203 224 231 232 264 308 319 336 348 352 406 462 464 528 609 616 638 672 696 812 924 928 957 1056 1218 1232 1276 1392 1624 1848 1914 2233 2436 2464 2552 2784 3248 3696 3828 4466 4872 5104 6496 6699 7392 7656 8932 9744 10208 13398 15312 17864 19488 26796 30624 35728 53592 71456 107184 214368