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Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively?
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Find the greatest no. That divides 85 and 72 leaving remainders 1 and ...
Explanation:
The greatest number that divides 85 and 72 leaving remainders 1 and 2 respectively can be found using the concept of the highest common factor (HCF) or greatest common divisor (GCD).
Finding the GCD using Remainder Theorem:
- Let x be the greatest number that divides both 85 and 72 leaving remainders 1 and 2 respectively.
- According to the Remainder Theorem, if a number divides two numbers leaving remainders r1 and r2 respectively, it must also divide their difference.
- Therefore, x must divide (85 - 1) = 84 and (72 - 2) = 70.
Calculating the GCD of 84 and 70:
- The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
- The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
- The common factors of 84 and 70 are 1, 2, and 7.
- Therefore, the greatest common factor (GCF) of 84 and 70 is 7.
Conclusion:
- The greatest number that divides 85 and 72 leaving remainders 1 and 2 respectively is 7.
The greatest number that divides 85 and 72 leaving remainders 1 and 2 respectively can be found using the concept of the highest common factor (HCF) or greatest common divisor (GCD).
Finding the GCD using Remainder Theorem:
- Let x be the greatest number that divides both 85 and 72 leaving remainders 1 and 2 respectively.
- According to the Remainder Theorem, if a number divides two numbers leaving remainders r1 and r2 respectively, it must also divide their difference.
- Therefore, x must divide (85 - 1) = 84 and (72 - 2) = 70.
Calculating the GCD of 84 and 70:
- The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
- The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70.
- The common factors of 84 and 70 are 1, 2, and 7.
- Therefore, the greatest common factor (GCF) of 84 and 70 is 7.
Conclusion:
- The greatest number that divides 85 and 72 leaving remainders 1 and 2 respectively is 7.
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Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively?
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Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively? 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 greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively?.
Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively? 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 greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the greatest no. That divides 85 and 72 leaving remainders 1 and 2 respectively?.
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