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Question

Help me with detail explanation to solve this Using divisibility tests determine whether 2, 15 and 468 is divided by 6, 8, 9 and 11.


Solution

The Rule for 6: The prime factors of 6are 2 and 3. So for a number to bedivisible by 6, it must also be divisible by 2 and 3.
The Rule for 8: If the last three digits of a whole number aredivisible by 8, then the entire number is divisible by 8.
A number is divisible by 9 if the sum of the digits is divisible by 9. 549 isdivisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 isdivisible by 9.Hence 549  is  divisible by 9
Here an easy way to test for divisibility by 11. Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.

So, for instance, 2728 has alternating sum of digits 2-7+2-8 = -11. Since -11 is divisible by 11, so is 2728.

Similarly, for 31415, the alternating sum of digits is 3-1+4-1+5 = 10. This is not divisible by 11, so neither is 31415.

Here 2 and 15 is not divisible by 6,8,9,and11 using the rules mentioned above.

468 is divisible by 6 as the number is divisible by both 3 and 2

468 is not divisible by 8 as the last three digits is not divisible by 8 

468 is divisible by 9 as the sum of the numbers is 4+6+8 = 18 which is divisible by 9

468 is not divisible by 11 as alternate sum is            4 -6 +8 =10 which is not divisible by 11

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