40320 has 96 divisors (see below), whose sum is σ = 159120. Its totient is φ = 9216.

The previous prime is 40289. The next prime is 40343. The reversal of 40320 is 2304.

Adding to 40320 its reverse (2304), we get a palindrome (42624).

It is a factorial (40320 = 8 ! = 1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5 ⋅ 6 ⋅ 7 ⋅ 8 ), and thus also a Jordan-Polya number.

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 (9).

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

It is a zygodrome in base 8.

It is a congruent number.

It is an unprimeable number.

40320 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 11 ways as a sum of consecutive naturals, for example, 5757 + ... + 5763.

2^{40320} is an apocalyptic number.

40320 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 40320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (79560).

40320 is an abundant number, since it is smaller than the sum of its proper divisors (118800).

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

40320 is a wasteful number, since it uses less digits than its factorization.

40320 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 9.

The square root of 40320 is about 200.7984063682. The cubic root of 40320 is about 34.2904755293.

The spelling of 40320 in words is "forty thousand, three hundred twenty", and thus it is an iban number.

Divisors: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 28 30 32 35 36 40 42 45 48 56 60 63 64 70 72 80 84 90 96 105 112 120 126 128 140 144 160 168 180 192 210 224 240 252 280 288 315 320 336 360 384 420 448 480 504 560 576 630 640 672 720 840 896 960 1008 1120 1152 1260 1344 1440 1680 1920 2016 2240 2520 2688 2880 3360 4032 4480 5040 5760 6720 8064 10080 13440 20160 40320

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