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420480 = 2732573
BaseRepresentation
bin1100110101010000000
3210100210100
41212222000
5101423410
613002400
73400614
oct1465200
9710710
10420480
11267a05
12183400
13119508
14ad344
15848c0
hex66a80

420480 has 96 divisors (see below), whose sum is σ = 1471860. Its totient is φ = 110592.

The previous prime is 420479. The next prime is 420481. The reversal of 420480 is 84024.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (420479) and next prime (420481).

It can be written as a sum of positive squares in 2 ways, for example, as 419904 + 576 = 648^2 + 24^2 .

It is a tau number, because it is divible by the number of its divisors (96).

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

It is not an unprimeable number, because it can be changed into a prime (420481) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 5724 + ... + 5796.

2420480 is an apocalyptic number.

420480 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 420480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (735930).

420480 is an abundant number, since it is smaller than the sum of its proper divisors (1051380).

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

420480 is a wasteful number, since it uses less digits than its factorization.

420480 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 18.

The square root of 420480 is about 648.4442921331. Note that the first 3 decimals coincide. The cubic root of 420480 is about 74.9172420485.

It can be divided in two parts, 420 and 480, that added together give a square (900 = 302).

The spelling of 420480 in words is "four hundred twenty thousand, four hundred eighty".

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 64 72 73 80 90 96 120 128 144 146 160 180 192 219 240 288 292 320 360 365 384 438 480 576 584 640 657 720 730 876 960 1095 1152 1168 1314 1440 1460 1752 1920 2190 2336 2628 2880 2920 3285 3504 4380 4672 5256 5760 5840 6570 7008 8760 9344 10512 11680 13140 14016 17520 21024 23360 26280 28032 35040 42048 46720 52560 70080 84096 105120 140160 210240 420480