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Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps
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Find the largest positive integer that will divide 122 , 150 , 115 lea...
Bhai sabhi number se jitna remainder chahiye utna minus kar ke hcf nikal lo. isse tumhara practice bhi ho jayega
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Find the largest positive integer that will divide 122 , 150 , 115 lea...
Step 1: Understand the Problem
To find the largest positive integer that divides the numbers 122, 150, and 115, leaving specific remainders, we first need to adjust each number by subtracting the corresponding remainder.
Step 2: Adjust the Numbers
- For 122 leaving a remainder of 5:
122 - 5 = 117
- For 150 leaving a remainder of 7:
150 - 7 = 143
- For 115 leaving a remainder of 11:
115 - 11 = 104
Now, we need to find the greatest common divisor (GCD) of the adjusted numbers: 117, 143, and 104.
Step 3: Find the GCD
- Factors of 117:
117 = 3 × 39 = 3 × 3 × 13
- Factors of 143:
143 = 11 × 13
- Factors of 104:
104 = 8 × 13 = 2 × 2 × 2 × 13
The common factor across all three numbers is 13.
Step 4: Conclusion
Thus, the largest positive integer that divides 122, 150, and 115, leaving remainders of 5, 7, and 11 respectively, is:
Final Answer: 13
To find the largest positive integer that divides the numbers 122, 150, and 115, leaving specific remainders, we first need to adjust each number by subtracting the corresponding remainder.
Step 2: Adjust the Numbers
- For 122 leaving a remainder of 5:
122 - 5 = 117
- For 150 leaving a remainder of 7:
150 - 7 = 143
- For 115 leaving a remainder of 11:
115 - 11 = 104
Now, we need to find the greatest common divisor (GCD) of the adjusted numbers: 117, 143, and 104.
Step 3: Find the GCD
- Factors of 117:
117 = 3 × 39 = 3 × 3 × 13
- Factors of 143:
143 = 11 × 13
- Factors of 104:
104 = 8 × 13 = 2 × 2 × 2 × 13
The common factor across all three numbers is 13.
Step 4: Conclusion
Thus, the largest positive integer that divides 122, 150, and 115, leaving remainders of 5, 7, and 11 respectively, is:
Final Answer: 13
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Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps
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Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps.
Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the largest positive integer that will divide 122 , 150 , 115 leaving remainder 5 , 7 , 11.Do with steps.
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