1680 has 40 divisors (see below), whose sum is σ = 5952. Its totient is φ = 384.

The previous prime is 1669. The next prime is 1693. The reversal of 1680 is 861.

It is a Cunningham number, because it is equal to 41^{2}-1.

1680 is an esthetic number in base 5, because in such base its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a plaindrome in base 9.

It is a nialpdrome in base 8, base 12, base 14 and base 15.

It is a zygodrome in base 9.

It is an unprimeable number.

1680 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 7 ways as a sum of consecutive naturals, for example, 237 + ... + 243.

1680 is a highly composite number, because it has more divisors than any smaller number.

1680 is a superabundant number, because it has a larger abundancy index than any smaller number.

1680 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1680 is the 24-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2976).

1680 is an abundant number, since it is smaller than the sum of its proper divisors (4272).

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

1680 is a wasteful number, since it uses less digits than its factorization.

1680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 48, while the sum is 15.

The square root of 1680 is about 40.9878030638. The cubic root of 1680 is about 11.8878439055.

Multiplying 1680 by its sum of digits (15), we get a triangular number (25200 = T_{224}).

Adding to 1680 its product of nonzero digits (48), we get a cube (1728 = 12^{3}).

The spelling of 1680 in words is "one thousand, six hundred eighty".

Divisors: 1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 28 30 35 40 42 48 56 60 70 80 84 105 112 120 140 168 210 240 280 336 420 560 840 1680

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