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To determine: Whether 120 is divisible by 2,3,5,6,or 10 by using
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Answer to Problem 4E
120 is divisible by 2,3,5,6 and 10
Explanation of Solution
Given information: Use divisibility rules to determine whether the number is divisible by 2,3,5,6, or 10.
Divisibility Rules
For 2: To test whether a number is divisible by 2, the number’s unit digit must be divisible by 2. If it is so then the given number is divisible by 2 else it is not. Also, the last digit of number should be 0,2,4,6,8 to get it divisible by 2.
For 3: If the sum of all digits of the given number is divisible by 3, then the number.
For 5: To test whether a number is divisible by 5 the number’s last digit must be divisible by 5. Also, the last digit of a number must be either 0 or 5 to get it divisible by 5.
For 6: A number is divisible by 6 if the number is divisible by both 2 and 3.
For 10: To test whether a number is divisible by 10 the number’s last digit must be divisible by 10 or the last digit of a number should be 0.
By implementing the above divisibility rules:
- The number 120 is divisible by 2 as the last digit is 0 which is divisible by 2.
- It is divisible by 3 because sum of all digits is 3 which is divisible by 3.
- It is divisible by 5 because the last digit is 0 which is divisible by 5.
- It is divisible by 6 because the number is divisible by both 2 and 3
- And in the last it is divisible by 10 because the last digit is 0.
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