16980

16980 is a six-digit integer. It follows the integer 16979 and precedes the integer 16981. In terms of its prime factorization, 16980 is equal to 2^2 * 3 * 5 * 11 * 13. This means it is a composite number. The number has a total of 24 divisors. Some of its divisors include 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 15, 20, 22, 26, 30, 33, 39, 44, 55, 60, 65, 66, 78, 110, 130, 132, 143, 156, 165, 176, 195, 220, 264, 286, 330, 390, 429, 440, 572, 605, 660, 715, 726, 1001, 1144, 1155, 1320, 1430, 1540, 1716, 1885, 2002, 2145, 2310, 2574, 2860, 3190, 3396, 3570, 3850, 4245, 4620, 5200, 5610, 5970, 6820, 8490, and 16980.

The number 16980 is an even number, as it is divisible by 2. It is also divisible by 5, meaning its last digit is either 0 or 5; in this case, it is 0. Being divisible by both 3 and 5 means it is also divisible by 15. Its divisibility by 11 can be checked using the alternating sum of its digits: 0 - 8 + 9 - 6 + 1 = -4, which is not divisible by 11. However, a calculation error occurred in the prime factorization. The correct prime factorization is 2^2 * 3 * 5 * 11 * 13. Let's re-verify the divisibility by 11. The alternating sum is 0 - 8 + 9 - 6 + 1 = -4. This indicates a potential issue with the provided prime factorization or the divisibility rule application. Let's use another method. 16980 / 11 = 1543.63..., so it is not divisible by 11.

Revisiting the prime factorization of 16980:

16980 / 10 = 1698

1698 / 2 = 849

849 / 3 = 283

283 is a prime number.

Therefore, the correct prime factorization of 16980 is 2^2 * 3 * 5 * 283. This implies 16980 is not divisible by 11 or 13. The number of divisors can be recalculated based on this corrected factorization. The sum of the exponents plus one, multiplied together: (2+1)*(1+1)*(1+1)*(1+1) = 3 * 2 * 2 * 2 = 24. The number of divisors remains 24.