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If 63, 87 and 123 are each divided by a number the remainder is same in each case. The greater possible value of the divisor must be
- a)6
- b)12
- c)16
- d)18
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If 63, 87 and 123 are each divided by a number the remainder is same i...
Le us say that the number ‘D’ divides 63, 87 and 123 to leave remainder ‘R’.
⇒ 63 – R, 87 – R and 123 – R are divisible by ‘D’
⇒ (87 – R) – (63 – R) and (123 – R) – (87 – R) are divisible by ‘D’
⇒ 24 and 36 are divisible by ‘D’
highest common factor of 24 and 36 = D = 12
⇒ 63 – R, 87 – R and 123 – R are divisible by ‘D’
⇒ (87 – R) – (63 – R) and (123 – R) – (87 – R) are divisible by ‘D’
⇒ 24 and 36 are divisible by ‘D’
highest common factor of 24 and 36 = D = 12
Most Upvoted Answer
If 63, 87 and 123 are each divided by a number the remainder is same i...
To find the greatest possible value of the divisor, we need to find the greatest common divisor (GCD) of the given numbers.
Finding the Remainder
Let's denote the divisor as 'd'. When we divide 63 by 'd', the remainder is r. Similarly, when we divide 87 and 123 by 'd', the remainders are also r.
So, we can express the three numbers as:
63 = kd + r ...(1)
87 = ld + r ...(2)
123 = md + r ...(3)
where k, l, and m are constants.
Subtracting equation (1) from equation (2), we get:
87 - 63 = ld + r - kd - r
24 = (l - k)d
Similarly, subtracting equation (1) from equation (3), we get:
123 - 63 = md + r - kd - r
60 = (m - k)d
Finding the GCD
Since the remainder is the same in each case, the GCD of 24 and 60 must also divide the difference between them, which is 36 (60 - 24).
Now, we need to find the factors of 36 to determine the possible values of 'd' (the divisor). The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Finding the Greatest Possible Divisor
We are looking for the greatest possible value of the divisor, so we need to find the largest factor of 36 that satisfies the given conditions.
From the given options, the largest factor of 36 is 12.
Conclusion
Therefore, the greatest possible value of the divisor is 12. Hence, the correct answer is option B.
Finding the Remainder
Let's denote the divisor as 'd'. When we divide 63 by 'd', the remainder is r. Similarly, when we divide 87 and 123 by 'd', the remainders are also r.
So, we can express the three numbers as:
63 = kd + r ...(1)
87 = ld + r ...(2)
123 = md + r ...(3)
where k, l, and m are constants.
Subtracting equation (1) from equation (2), we get:
87 - 63 = ld + r - kd - r
24 = (l - k)d
Similarly, subtracting equation (1) from equation (3), we get:
123 - 63 = md + r - kd - r
60 = (m - k)d
Finding the GCD
Since the remainder is the same in each case, the GCD of 24 and 60 must also divide the difference between them, which is 36 (60 - 24).
Now, we need to find the factors of 36 to determine the possible values of 'd' (the divisor). The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Finding the Greatest Possible Divisor
We are looking for the greatest possible value of the divisor, so we need to find the largest factor of 36 that satisfies the given conditions.
From the given options, the largest factor of 36 is 12.
Conclusion
Therefore, the greatest possible value of the divisor is 12. Hence, the correct answer is option B.
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If 63, 87 and 123 are each divided by a number the remainder is same in each case. The greater possible value of the divisor must bea)6b)12c)16d)18Correct answer is option 'B'. Can you explain this answer?
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If 63, 87 and 123 are each divided by a number the remainder is same in each case. The greater possible value of the divisor must bea)6b)12c)16d)18Correct answer is option 'B'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about If 63, 87 and 123 are each divided by a number the remainder is same in each case. The greater possible value of the divisor must bea)6b)12c)16d)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 63, 87 and 123 are each divided by a number the remainder is same in each case. The greater possible value of the divisor must bea)6b)12c)16d)18Correct answer is option 'B'. Can you explain this answer?.
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