Final answer:
To check the divisibility of numbers by 2, 3, 4, 5, 6, 9, and 10, we use specific rules. For instance, a number ending with an even digit is divisible by 2. The divisibility of 1236, 4050, and 8928 representative findings are discussed in the example.
Step-by-step explanation:
In mathematics, when working with divisibility rules, it's important to be able to determine whether a given number is divisible by another without performing the actual division. Here, we're going to list three numbers with a minimum of four digits and check their divisibility by 2, 3, 4, 5, 6, 9, and 10.
Let's start with our numbers:
Divisibility rules:
-
- For 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
-
- For 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
-
- For 4: A number is divisible by 4 if its last two digits form a number that's divisible by 4.
-
- For 5: A number is divisible by 5 if its last digit is 0 or 5.
-
- For 6: A number is divisible by 6 if it satisfies the divisibility rules for both 2 and 3.
-
- For 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
-
- For 10: A number is divisible by 10 if its last digit is 0.
Checking divisibility:
-
- 1236: Divisible by 2 (last digit is 6), 3 (sum is 12), 4 (36 is divisible by 4), not divisible by 5, divisible by 6 (meets rules for both 2 and 3), not divisible by 9, not divisible by 10.
-
- 4050: Divisible by 2 (last digit is 0), 3 (sum is 9), 4 (50 is not divisible by 4), divisible by 5 (last digit is 0), divisible by 6 (meets rules for both 2 and 3), divisible by 9 (sum is 9), divisible by 10 (last digit is 0).
-
- 8928: Divisible by 2 (last digit is 8), not divisible by 3 (sum is 27), divisible by 4 (28 is divisible by 4), not divisible by 5, not divisible by 6 (does not meet rule for 3), divisible by 9 (sum is 27), not divisible by 10.