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468864 = 27321137
BaseRepresentation
bin1110010011110000000
3212211011100
41302132000
5110000424
614014400
73661644
oct1623600
9784140
10468864
112a02a0
121a7400
13135546
14c2c24
1593dc9
hex72780

468864 has 96 divisors (see below), whose sum is σ = 1511640. Its totient is φ = 138240.

The previous prime is 468859. The next prime is 468869.

468864 is nontrivially palindromic in base 10.

It is an interprime number because it is at equal distance from previous prime (468859) and next prime (468869).

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 (36).

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

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (468869) by changing a digit.

468864 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 11 ways as a sum of consecutive naturals, for example, 12654 + ... + 12690.

2468864 is an apocalyptic number.

468864 is a gapful number since it is divisible by the number (44) 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 468864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (755820).

468864 is an abundant number, since it is smaller than the sum of its proper divisors (1042776).

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

468864 is a wasteful number, since it uses less digits than its factorization.

468864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 68 (or 53 counting only the distinct ones).

The product of its digits is 36864, while the sum is 36.

The square root of 468864 is about 684.7364456490. The cubic root of 468864 is about 77.6871094630.

The spelling of 468864 in words is "four hundred sixty-eight thousand, eight hundred sixty-four".

Divisors: 1 2 3 4 6 8 9 11 12 16 18 22 24 32 33 36 37 44 48 64 66 72 74 88 96 99 111 128 132 144 148 176 192 198 222 264 288 296 333 352 384 396 407 444 528 576 592 666 704 792 814 888 1056 1152 1184 1221 1332 1408 1584 1628 1776 2112 2368 2442 2664 3168 3256 3552 3663 4224 4736 4884 5328 6336 6512 7104 7326 9768 10656 12672 13024 14208 14652 19536 21312 26048 29304 39072 42624 52096 58608 78144 117216 156288 234432 468864