Class 10 Exam > Class 10 Questions > find the largest positive integer that will d...
Start Learning for Free
find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor
?
Most Upvoted Answer
find the largest positive integer that will divide 122.150 .115.leavin...
Numbers are 122 150 and 115 Remainder are 5 7 and 11 resp Now , 122-5= 117 150-7= 143 115-11= 104 HCF of 117 143 and 104 is 13 Therefore 13 is the largest number which divides 112 150 and 115 leaving remainder 5 7 and 11 resp.
Community Answer
find the largest positive integer that will divide 122.150 .115.leavin...
To find the largest positive integer that will divide 122, 150, and 115 leaving remainders 5, 7, and 11 respectively, we can follow these steps:
Understand the Problem
- We need to find a number 'x' such that:
- 122 - 5 = 117 is divisible by 'x'
- 150 - 7 = 143 is divisible by 'x'
- 115 - 11 = 104 is divisible by 'x'
Thus, we need to find the Highest Common Factor (HCF) of the numbers 117, 143, and 104.
Calculate the Differences
- The modified numbers to consider are:
- 117
- 143
- 104
Find the HCF
- To find the HCF, we can use the prime factorization method or the division method.
Prime Factorization
- 117:
- 117 = 3 × 39
- 39 = 3 × 13
- So, 117 = 3^2 × 13
- 143:
- 143 = 11 × 13
- 104:
- 104 = 8 × 13
- 8 = 2^3
- So, 104 = 2^3 × 13
Identify Common Factors
- The only common prime factor among the numbers is 13.
Conclusion
- Therefore, the largest positive integer that will divide 122, 150, and 115, leaving remainders 5, 7, and 11 respectively, is 13.
Understand the Problem
- We need to find a number 'x' such that:
- 122 - 5 = 117 is divisible by 'x'
- 150 - 7 = 143 is divisible by 'x'
- 115 - 11 = 104 is divisible by 'x'
Thus, we need to find the Highest Common Factor (HCF) of the numbers 117, 143, and 104.
Calculate the Differences
- The modified numbers to consider are:
- 117
- 143
- 104
Find the HCF
- To find the HCF, we can use the prime factorization method or the division method.
Prime Factorization
- 117:
- 117 = 3 × 39
- 39 = 3 × 13
- So, 117 = 3^2 × 13
- 143:
- 143 = 11 × 13
- 104:
- 104 = 8 × 13
- 8 = 2^3
- So, 104 = 2^3 × 13
Identify Common Factors
- The only common prime factor among the numbers is 13.
Conclusion
- Therefore, the largest positive integer that will divide 122, 150, and 115, leaving remainders 5, 7, and 11 respectively, is 13.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers?
Question Description
find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? 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 remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? 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 remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers?.
find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? 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 remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? 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 remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers?.
Solutions for find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? defined & explained in the simplest way possible. Besides giving the explanation of
find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers?, a detailed solution for find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? has been provided alongside types of find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? theory, EduRev gives you an
ample number of questions to practice find the largest positive integer that will divide 122.150 .115.leaving remainders 5.7.11respectively.using HCF by taking common factor Related: Ex 1.3 NCERT Solutions - Real Numbers? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup