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What would be the greatest number that divides 14, 20, and 32 leaving the same remainder?
- a)3
- b)6
- c)12
- d)14
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What would be the greatest number that divides 14, 20, and 32 leaving ...
Here, the number which divides 14, 20, and 32 leaves the same remainder.
∴ We will be using HCF model 2
The required number will be the HCF of (20 - 14), (32 - 20), and (32 - 14).
i.e. HCF (6, 12, 18)
which will be 6.
Therefore, the required number is 6.
∴ We will be using HCF model 2
The required number will be the HCF of (20 - 14), (32 - 20), and (32 - 14).
i.e. HCF (6, 12, 18)
which will be 6.
Therefore, the required number is 6.
Most Upvoted Answer
What would be the greatest number that divides 14, 20, and 32 leaving ...
Solution:
To find the greatest number that divides 14, 20, and 32 leaving the same remainder, we need to find the common difference between these numbers.
Step 1: Find the remainders
Let's assume the common remainder be x.
The remainder when 14 is divided by the required number will be x.
Therefore, the first number that leaves the same remainder x is 14 + x.
Similarly, the second number that leaves the same remainder x is 20 + x.
The third number that leaves the same remainder x is 32 + x.
Step 2: Find the common difference
The required number should divide the difference between any two pairs of these numbers.
So, we can find the common difference by taking the difference between any two pairs of these numbers.
(20 + x) - (14 + x) = 6
(32 + x) - (20 + x) = 12
We can see that the common difference between these pairs is 6.
Therefore, the greatest number that divides 14, 20, and 32 leaving the same remainder is the HCF of (6, 14).
Step 3: Find the HCF
We can find the HCF of 6 and 14 by prime factorization.
6 = 2 x 3
14 = 2 x 7
The common factor between 6 and 14 is 2.
Therefore, the HCF of 6 and 14 is 2 x 1 = 2.
Therefore, the correct option is (b) 6.
To find the greatest number that divides 14, 20, and 32 leaving the same remainder, we need to find the common difference between these numbers.
Step 1: Find the remainders
Let's assume the common remainder be x.
The remainder when 14 is divided by the required number will be x.
Therefore, the first number that leaves the same remainder x is 14 + x.
Similarly, the second number that leaves the same remainder x is 20 + x.
The third number that leaves the same remainder x is 32 + x.
Step 2: Find the common difference
The required number should divide the difference between any two pairs of these numbers.
So, we can find the common difference by taking the difference between any two pairs of these numbers.
(20 + x) - (14 + x) = 6
(32 + x) - (20 + x) = 12
We can see that the common difference between these pairs is 6.
Therefore, the greatest number that divides 14, 20, and 32 leaving the same remainder is the HCF of (6, 14).
Step 3: Find the HCF
We can find the HCF of 6 and 14 by prime factorization.
6 = 2 x 3
14 = 2 x 7
The common factor between 6 and 14 is 2.
Therefore, the HCF of 6 and 14 is 2 x 1 = 2.
Therefore, the correct option is (b) 6.
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What would be the greatest number that divides 14, 20, and 32 leaving ...
6, because it divides 14,20and 32 leaving 2 as reminder...
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What would be the greatest number that divides 14, 20, and 32 leaving the same remainder?a)3b)6c)12d)14Correct answer is option 'B'. Can you explain this answer?
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What would be the greatest number that divides 14, 20, and 32 leaving the same remainder?a)3b)6c)12d)14Correct answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about What would be the greatest number that divides 14, 20, and 32 leaving the same remainder?a)3b)6c)12d)14Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What would be the greatest number that divides 14, 20, and 32 leaving the same remainder?a)3b)6c)12d)14Correct answer is option 'B'. Can you explain this answer?.
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