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A number is divisible by 4 if its
- a)last digit is 0
- b)last digit is 4
- c)last two digits are divisible by 4
- d)last digit is 8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A number is divisible by 4 if itsa)last digit is 0b)last digit is 4c)l...
Whole numbers are divisible by 4 if the number formed by the last two individual digits is evenly divisible by 4.
For example, the number formed by the last two digits of the number 3628 is 28, which is evenly divisible by 4 so the number 3628 is evenly divisible by 4.
Most Upvoted Answer
A number is divisible by 4 if itsa)last digit is 0b)last digit is 4c)l...
Explanation:
A number is divisible by 4 if and only if the last two digits of the number are divisible by 4. This is because 4 is a multiple of 2, and any number that is divisible by 2 will have its last digit divisible by 2.
Proof:
Let's consider a number with the last two digits as "xy". This can be written as 10x + y.
If 10x + y is divisible by 4, it means that (10x + y) % 4 = 0.
We can rewrite this equation as:
(10x % 4 + y % 4) % 4 = 0.
Since 10 % 4 = 2, we can substitute this in the equation:
(2x + y % 4) % 4 = 0.
Now, let's consider all the possibilities for the value of y % 4:
1. If y % 4 = 0, then the equation becomes:
(2x + 0) % 4 = 0.
This means that 2x % 4 = 0, which is true for any even value of x.
2. If y % 4 = 1, then the equation becomes:
(2x + 1) % 4 = 0.
This equation is not possible because 2x + 1 will always be odd, and an odd number cannot be divisible by 4.
3. If y % 4 = 2, then the equation becomes:
(2x + 2) % 4 = 0.
Simplifying this equation, we get:
2x % 4 = 0, which is true for any even value of x.
4. If y % 4 = 3, then the equation becomes:
(2x + 3) % 4 = 0.
This equation is not possible because 2x + 3 will always be odd, and an odd number cannot be divisible by 4.
From the above analysis, we can conclude that a number is divisible by 4 if and only if the last two digits of the number are divisible by 4. Hence, option C is the correct answer.
A number is divisible by 4 if and only if the last two digits of the number are divisible by 4. This is because 4 is a multiple of 2, and any number that is divisible by 2 will have its last digit divisible by 2.
Proof:
Let's consider a number with the last two digits as "xy". This can be written as 10x + y.
If 10x + y is divisible by 4, it means that (10x + y) % 4 = 0.
We can rewrite this equation as:
(10x % 4 + y % 4) % 4 = 0.
Since 10 % 4 = 2, we can substitute this in the equation:
(2x + y % 4) % 4 = 0.
Now, let's consider all the possibilities for the value of y % 4:
1. If y % 4 = 0, then the equation becomes:
(2x + 0) % 4 = 0.
This means that 2x % 4 = 0, which is true for any even value of x.
2. If y % 4 = 1, then the equation becomes:
(2x + 1) % 4 = 0.
This equation is not possible because 2x + 1 will always be odd, and an odd number cannot be divisible by 4.
3. If y % 4 = 2, then the equation becomes:
(2x + 2) % 4 = 0.
Simplifying this equation, we get:
2x % 4 = 0, which is true for any even value of x.
4. If y % 4 = 3, then the equation becomes:
(2x + 3) % 4 = 0.
This equation is not possible because 2x + 3 will always be odd, and an odd number cannot be divisible by 4.
From the above analysis, we can conclude that a number is divisible by 4 if and only if the last two digits of the number are divisible by 4. Hence, option C is the correct answer.
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Community Answer
A number is divisible by 4 if itsa)last digit is 0b)last digit is 4c)l...
Answer is option c) last two digits are divisible by 4
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
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