| Base | Representation |
|---|---|
| bin | 11000110000011… |
| … | …010011100010000 |
| 3 | 1001221112200101221 |
| 4 | 120300122130100 |
| 5 | 1322312010100 |
| 6 | 105114134424 |
| 7 | 13202240422 |
| oct | 3060323420 |
| 9 | 1057480357 |
| 10 | 415344400 |
| 11 | 1a34a6439 |
| 12 | b7121414 |
| 13 | 68084923 |
| 14 | 3d23a812 |
| 15 | 266e501a |
| hex | 18c1a710 |
415344400 has 45 divisors (see below), whose sum is σ = 998845141. Its totient is φ = 165974720.
The previous prime is 415344383. The next prime is 415344401. The reversal of 415344400 is 4443514.
The square root of 415344400 is 20380.
It is a perfect power (a square), and thus also a powerful number.
It can be written as a sum of positive squares in only one way, i.e., 149523984 + 265820416 = 12228^2 + 16304^2 .
It is a super-2 number, since 2×4153444002 = 345021941222720000, which contains 22 as substring.
It is a Harshad number since it is a multiple of its sum of digits (25).
It is a Duffinian number.
It is not an unprimeable number, because it can be changed into a prime (415344401) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (11) of ones.
It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 407091 + ... + 408109.
Almost surely, 2415344400 is an apocalyptic number.
415344400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.
415344400 is the 20380-th square number.
It is an amenable number.
415344400 is an abundant number, since it is smaller than the sum of its proper divisors (583500741).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
415344400 is an equidigital number, since it uses as much as digits as its factorization.
415344400 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 2056 (or 1026 counting only the distinct ones).
The product of its (nonzero) digits is 3840, while the sum is 25.
The cubic root of 415344400 is about 746.1098722419.
Multiplying 415344400 by its sum of digits (25), we get a square (10383610000 = 1019002).
415344400 divided by its sum of digits (25) gives a square (16613776 = 40762).
Adding to 415344400 its reverse (4443514), we get a palindrome (419787914).
The spelling of 415344400 in words is "four hundred fifteen million, three hundred forty-four thousand, four hundred".
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