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Question
Use the divisibility tests to determine whether the following numbers are divisible by 2, 3, 4, 5, 6, 9 or 11.
(7) 504
(7) 504
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Solution
We can observe that the digit in the units place is 4.
If a number has 0, 2, 4, 6 or 8 in its units place, then the number is divisible by 2. So, the number 504 is divisible by 2.
The sum of the digits 5, 0 and 4 is 9, which is divisible by both 3 and 9.
If the sum of all the digits in a number is divisible by 3 and 9, then the number is divisible by both 3 and 9. So, the number 504 is divisible by both 3 and 9.
The number formed by the digits in the tens and units places is 04, which is divisible by 4.
If the number formed by the digits in the tens and units places of a number is divisible by 4, then the number is divisible by 4. So, the number 504 is divisible by 4.
If a number is divisible by both 2 and 3, then the number is divisible by 6. So, the number 504 is also divisible by 6.
Hence, the number 504 is divisible by 2, 3, 4, 6 and 9.
If a number has 0, 2, 4, 6 or 8 in its units place, then the number is divisible by 2. So, the number 504 is divisible by 2.
The sum of the digits 5, 0 and 4 is 9, which is divisible by both 3 and 9.
If the sum of all the digits in a number is divisible by 3 and 9, then the number is divisible by both 3 and 9. So, the number 504 is divisible by both 3 and 9.
The number formed by the digits in the tens and units places is 04, which is divisible by 4.
If the number formed by the digits in the tens and units places of a number is divisible by 4, then the number is divisible by 4. So, the number 504 is divisible by 4.
If a number is divisible by both 2 and 3, then the number is divisible by 6. So, the number 504 is also divisible by 6.
Hence, the number 504 is divisible by 2, 3, 4, 6 and 9.
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