• 840 can be written using four 4's:

840 has 32 divisors (see below), whose sum is σ = 2880. Its totient is φ = 192.

The previous prime is 839. The next prime is 853. The reversal of 840 is 48.

It is a Cunningham number, because it is equal to 29^{2}-1.

It is a Harshad number since it is a multiple of its sum of digits (12).

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

840 is an idoneal number.

It is a straight-line number, since its digits are in arithmetic progression.

It is a plaindrome in base 9 and base 16.

It is a nialpdrome in base 10 and base 14.

It is a zygodrome in base 9.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 840.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 117 + ... + 123.

It is an arithmetic number, because the mean of its divisors is an integer number (90).

840 is a highly composite number, because it has more divisors than any smaller number.

840 is a superabundant number, because it has a larger abundancy index than any smaller number.

2^{840} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 840, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1440).

840 is an abundant number, since it is smaller than the sum of its proper divisors (2040).

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

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

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

The sum of its prime factors is 21 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 12.

The square root of 840 is about 28.9827534924. The cubic root of 840 is about 9.4353879606.

Subtracting from 840 its sum of digits (12), we obtain a palindrome (828).

Subtracting from 840 its product of nonzero digits (32), we obtain a palindrome (808).

Adding to 840 its reverse (48), we get a palindrome (888).

The spelling of 840 in words is "eight hundred forty", and thus it is an aban number.

Divisors: 1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28 30 35 40 42 56 60 70 84 105 120 140 168 210 280 420 840

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