414000 has 120 divisors (see below), whose sum is σ = 1508832. Its totient is φ = 105600.

The previous prime is 413981. The next prime is 414013. The reversal of 414000 is 414.

Adding to 414000 its reverse (414), we get a palindrome (414414).

414000 divided by its reverse (414) gives a cube (1000 = 10^{3}).

414000 = 123^{2} + 124^{2} + ... + 145^{2}.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is an unprimeable number.

414000 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 23 ways as a sum of consecutive naturals, for example, 17989 + ... + 18011.

2^{414000} is an apocalyptic number.

414000 is a gapful number since it is divisible by the number (40) 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 414000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (754416).

414000 is an abundant number, since it is smaller than the sum of its proper divisors (1094832).

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

414000 is a wasteful number, since it uses less digits than its factorization.

414000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 52 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The square root of 414000 is about 643.4283176858. The cubic root of 414000 is about 74.5303991372.

The spelling of 414000 in words is "four hundred fourteen thousand", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 23 24 25 30 36 40 45 46 48 50 60 69 72 75 80 90 92 100 115 120 125 138 144 150 180 184 200 207 225 230 240 250 276 300 345 360 368 375 400 414 450 460 500 552 575 600 690 720 750 828 900 920 1000 1035 1104 1125 1150 1200 1380 1500 1656 1725 1800 1840 2000 2070 2250 2300 2760 2875 3000 3312 3450 3600 4140 4500 4600 5175 5520 5750 6000 6900 8280 8625 9000 9200 10350 11500 13800 16560 17250 18000 20700 23000 25875 27600 34500 41400 46000 51750 69000 82800 103500 138000 207000 414000

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