414720 has 110 divisors (see below), whose sum is σ = 1486122. Its totient is φ = 110592.

The previous prime is 414709. The next prime is 414721. The reversal of 414720 is 27414.

It can be divided in two parts, 41 and 4720, that added together give a square (4761 = 69^{2}).

It is a happy number.

It is a Jordan-Polya number, since it can be written as 6! ⋅ (4!)^{2}.

It can be written as a sum of positive squares in only one way, i.e., 331776 + 82944 = 576^2 + 288^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 16.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 414693 and 414702.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414721) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 82942 + ... + 82946.

414720 is a Friedman number, since it can be written as 20*(7+4+1)^4, using all its digits and the basic arithmetic operations.

2^{414720} is an apocalyptic number.

414720 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 414720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (743061).

414720 is an abundant number, since it is smaller than the sum of its proper divisors (1071402).

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

414720 is an equidigital number, since it uses as much as digits as its factorization.

414720 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 37 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 18.

The square root of 414720 is about 643.9875775199. The cubic root of 414720 is about 74.5735801429.

The spelling of 414720 in words is "four hundred fourteen thousand, seven hundred twenty", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 64 72 80 81 90 96 108 120 128 135 144 160 162 180 192 216 240 256 270 288 320 324 360 384 405 432 480 512 540 576 640 648 720 768 810 864 960 1024 1080 1152 1280 1296 1440 1536 1620 1728 1920 2160 2304 2560 2592 2880 3072 3240 3456 3840 4320 4608 5120 5184 5760 6480 6912 7680 8640 9216 10368 11520 12960 13824 15360 17280 20736 23040 25920 27648 34560 41472 46080 51840 69120 82944 103680 138240 207360 414720

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