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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for "HCF and LCM" under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.
Q. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
- a)4
- b)7
- c)9
- d)13
Correct answer is option 'A'. Can you explain this answer?
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are av...
To find the greatest number that will divide 43, 91, and 183 and leave the same remainder in each case, we need to find the highest common factor (HCF) of these numbers.
Let's start by finding the factors of each number:
Factors of 43: 1, 43
Factors of 91: 1, 7, 13, 91
Factors of 183: 1, 3, 61, 183
Now, let's analyze the remainders when each of these numbers is divided by a certain number:
When divided by 4:
43 leaves a remainder of 3
91 leaves a remainder of 3
183 leaves a remainder of 3
When divided by 7:
43 leaves a remainder of 1
91 leaves a remainder of 0
183 leaves a remainder of 0
When divided by 9:
43 leaves a remainder of 7
91 leaves a remainder of 1
183 leaves a remainder of 0
When divided by 13:
43 leaves a remainder of 4
91 leaves a remainder of 0
183 leaves a remainder of 0
From the above analysis, we can see that the only common remainder in all cases is 0.
Therefore, the greatest number that will divide 43, 91, and 183 and leave the same remainder in each case is the HCF of these numbers.
HCF of 43, 91, and 183 = 1 (as it is the only number that divides all three numbers without leaving any remainder)
Hence, the correct answer is option A) 4.
Let's start by finding the factors of each number:
Factors of 43: 1, 43
Factors of 91: 1, 7, 13, 91
Factors of 183: 1, 3, 61, 183
Now, let's analyze the remainders when each of these numbers is divided by a certain number:
When divided by 4:
43 leaves a remainder of 3
91 leaves a remainder of 3
183 leaves a remainder of 3
When divided by 7:
43 leaves a remainder of 1
91 leaves a remainder of 0
183 leaves a remainder of 0
When divided by 9:
43 leaves a remainder of 7
91 leaves a remainder of 1
183 leaves a remainder of 0
When divided by 13:
43 leaves a remainder of 4
91 leaves a remainder of 0
183 leaves a remainder of 0
From the above analysis, we can see that the only common remainder in all cases is 0.
Therefore, the greatest number that will divide 43, 91, and 183 and leave the same remainder in each case is the HCF of these numbers.
HCF of 43, 91, and 183 = 1 (as it is the only number that divides all three numbers without leaving any remainder)
Hence, the correct answer is option A) 4.
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Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for"HCF and LCM"under Quantitative Aptitude. You can practice these practice quizzes as per your speed and improvise the topic. The same topic is covered under various competitive examinations like - CAT, GMAT, Bank PO, SSC and other competitive examinations.Q. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.a)4b)7c)9d)13Correct answer is option 'A'. Can you explain this answer?
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