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419904 = 2638
BaseRepresentation
bin1100110100001000000
3210100000000
41212201000
5101414104
613000000
73366132
oct1464100
9710000
10419904
11267531
12183000
13119184
14ad052
1584639
hex66840

419904 has 63 divisors (see below), whose sum is σ = 1249807. Its totient is φ = 139968.

The previous prime is 419893. The next prime is 419921. The reversal of 419904 is 409914.

Multipling 419904 by its product of nonzero digits (1296), we get a square (544195584 = 233282).

419904 divided by its product of nonzero digits (1296) gives a square (324 = 182).

The square root of 419904 is 648.

It is a perfect power (a square), and thus also a powerful number.

It is an ABA number since it can be written as A⋅BA, here for A=4, B=18.

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

It is a Duffinian number.

It is a nialpdrome in base 9.

It is an unprimeable number.

419904 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 8 ways as a sum of consecutive naturals, for example, 139967 + 139968 + 139969.

419904 is a Friedman number, since it can be written as (9+9)^(4*(1+0))*4, using all its digits and the basic arithmetic operations.

2419904 is an apocalyptic number.

419904 is the 648-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 419904

419904 is an abundant number, since it is smaller than the sum of its proper divisors (829903).

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

419904 is an frugal number, since it uses more digits than its factorization.

419904 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The cubic root of 419904 is about 74.8830176299.

The spelling of 419904 in words is "four hundred nineteen thousand, nine hundred four".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 144 162 192 216 243 288 324 432 486 576 648 729 864 972 1296 1458 1728 1944 2187 2592 2916 3888 4374 5184 5832 6561 7776 8748 11664 13122 15552 17496 23328 26244 34992 46656 52488 69984 104976 139968 209952 419904