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314496 = 2733713
BaseRepresentation
bin1001100110010000000
3120222102000
41030302000
540030441
610424000
72446620
oct1146200
9528360
10314496
111a5316
12132000
13b01c0
1482880
15632b6
hex4cc80

314496 has 128 divisors (see below), whose sum is σ = 1142400. Its totient is φ = 82944.

The previous prime is 314491. The next prime is 314497. The reversal of 314496 is 694413.

It can be divided in two parts, 3144 and 96, that added together give a triangular number (3240 = T80).

314496 = 63 + 73 + ... + 333.

It is a tau number, because it is divible by the number of its divisors (128).

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is a taxicab number since it can be written as a sum of two cubes in more than one way. Here 314496 = 43 + 683 = 303 + 663.

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 314496.

It is not an unprimeable number, because it can be changed into a prime (314491) by changing a digit.

314496 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, 24186 + ... + 24198.

It is an arithmetic number, because the mean of its divisors is an integer number (8925).

314496 is a Friedman number, since it can be written as 91*6^3*4*4, using all its digits and the basic arithmetic operations.

2314496 is an apocalyptic number.

314496 is a gapful number since it is divisible by the number (36) 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 314496, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (571200).

314496 is an abundant number, since it is smaller than the sum of its proper divisors (827904).

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

314496 is a wasteful number, since it uses less digits than its factorization.

314496 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 25 counting only the distinct ones).

The product of its digits is 2592, while the sum is 27.

The square root of 314496 is about 560.7994293863. The cubic root of 314496 is about 68.0046132972.

The spelling of 314496 in words is "three hundred fourteen thousand, four hundred ninety-six".

Divisors: 1 2 3 4 6 7 8 9 12 13 14 16 18 21 24 26 27 28 32 36 39 42 48 52 54 56 63 64 72 78 84 91 96 104 108 112 117 126 128 144 156 168 182 189 192 208 216 224 234 252 273 288 312 336 351 364 378 384 416 432 448 468 504 546 576 624 672 702 728 756 819 832 864 896 936 1008 1092 1152 1248 1344 1404 1456 1512 1638 1664 1728 1872 2016 2184 2457 2496 2688 2808 2912 3024 3276 3456 3744 4032 4368 4914 4992 5616 5824 6048 6552 7488 8064 8736 9828 11232 11648 12096 13104 14976 17472 19656 22464 24192 26208 34944 39312 44928 52416 78624 104832 157248 314496