Final answer:
Divisibility rules are shortcuts that help you determine whether a given number is divisible by another. Rules for numbers such as 9, 10, 11, and so on, typically involve checks like summing digits, looking at the last digit, or applying multiple rules in conjunction.
Step-by-step explanation:
Divisibility rules allow us to determine if a number is divisible by another without performing the division. Below are the divisibility rules for the numbers 9,10,11,12,13,14,15,16,17,18,19,20, and 66:
- Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- Divisibility rule for 10: A number is divisible by 10 if it ends in 0.
- Divisibility rule for 11: A number is divisible by 11 if the alternating sum of its digits (subtracting every second digit from the sum of the other digits) is zero or a multiple of 11.
- Divisibility rule for 12: A number is divisible by 12 if it is divisible by both 3 and 4.
- Divisibility rule for 13: There's no simple rule for 13, but a number like 26, where 2 + (4×13) = 54, which is divisible by 13, indicates divisibility.
- Divisibility rule for 14: A number is divisible by 14 if it is divisible by both 2 and 7.
- Divisibility rule for 15: A number is divisible by 15 if it is divisible by both 3 and 5.
- Divisibility rule for 16: A number is divisible by 16 if the last four digits form a number divisible by 16.
- Divisibility rule for 17: There's no simple rule for 17, but you can subtract 5 times the last digit from the remaining leading truncated number, and if the result is divisible by 17, so is the original number.
- Divisibility rule for 18: A number is divisible by 18 if it is divisible by both 2 and 9.
- Divisibility rule for 19: There's no simple rule for 19, but a pattern similar to 13's rule can apply, like 2 + (2×19) for 38, which gives 40, divisible by 19.
- Divisibility rule for 20: A number is divisible by 20 if it ends in a 0 and its tens digit is even.
- Divisibility rule for 66: A number is divisible by 66 if it is divisible by both 6 and 11.
These rules are part of the fundamental structure of mathematics, which are universally valid and can lead to correct conclusions regardless of the context or magnitude of the numbers.