7560 has 64 divisors (see below), whose sum is σ = 28800. Its totient is φ = 1728.

The previous prime is 7559. The next prime is 7561. The reversal of 7560 is 657.

Multipling 7560 by its product of nonzero digits (210), we get a square (1587600 = 1260^{2}).

7560 divided by its product of nonzero digits (210) gives a triangular number (36 = T_{8}).

Subtracting from 7560 its reverse (657), we obtain a triangular number (6903 = T_{117}).

It is an interprime number because it is at equal distance from previous prime (7559) and next prime (7561).

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

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7561) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1077 + ... + 1083.

It is an arithmetic number, because the mean of its divisors is an integer number (450).

7560 is a highly composite number, because it has more divisors than any smaller number.

2^{7560} is an apocalyptic number.

7560 is a gapful number since it is divisible by the number (70) 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 7560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14400).

7560 is an abundant number, since it is smaller than the sum of its proper divisors (21240).

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

7560 is a wasteful number, since it uses less digits than its factorization.

7560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 27 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 210, while the sum is 18.

The square root of 7560 is about 86.9482604771. The cubic root of 7560 is about 19.6263978611.

The spelling of 7560 in words is "seven thousand, five hundred sixty".

Divisors: 1 2 3 4 5 6 7 8 9 10 12 14 15 18 20 21 24 27 28 30 35 36 40 42 45 54 56 60 63 70 72 84 90 105 108 120 126 135 140 168 180 189 210 216 252 270 280 315 360 378 420 504 540 630 756 840 945 1080 1260 1512 1890 2520 3780 7560

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