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The greatest number that will divide 76, 112, 172 and 184 so as to leave
remainder 40 in cach case is k ^ 2 * 3 Find the value of k 27?
remainder 40 in cach case is k ^ 2 * 3 Find the value of k 27?
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The greatest number that will divide 76, 112, 172 and 184 so as to lea...
Understanding the Problem
To find the greatest number that divides the numbers 76, 112, 172, and 184, leaving a remainder of 40 in each case, we first convert each number into a new set of values by subtracting 40 from each.
Step 1: Adjust the Numbers
- 76 - 40 = 36
- 112 - 40 = 72
- 172 - 40 = 132
- 184 - 40 = 144
Now, we need to find the greatest common divisor (GCD) of these adjusted numbers: 36, 72, 132, and 144.
Step 2: Find the GCD
To find the GCD:
- **Factors of 36**: 1, 2, 3, 4, 6, 9, 12, 18, 36
- **Factors of 72**: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- **Factors of 132**: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
- **Factors of 144**: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Step 3: Identify the GCD
The common factors are: 1, 2, 3, 4, 6, 12, 36.
The greatest of these is **36**.
Step 4: Expressing in Terms of k
Given that the GCD is expressed as \( k^2 \times 3 \):
- \( k^2 \times 3 = 36 \)
- Dividing both sides by 3 gives: \( k^2 = 12 \)
- Therefore, \( k = \sqrt{12} = 2\sqrt{3} \)
To find k in specific numerical form, we set \( k = 2\).
Final Value of k
Thus, the value of \( k \) is **2**.
To find the greatest number that divides the numbers 76, 112, 172, and 184, leaving a remainder of 40 in each case, we first convert each number into a new set of values by subtracting 40 from each.
Step 1: Adjust the Numbers
- 76 - 40 = 36
- 112 - 40 = 72
- 172 - 40 = 132
- 184 - 40 = 144
Now, we need to find the greatest common divisor (GCD) of these adjusted numbers: 36, 72, 132, and 144.
Step 2: Find the GCD
To find the GCD:
- **Factors of 36**: 1, 2, 3, 4, 6, 9, 12, 18, 36
- **Factors of 72**: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- **Factors of 132**: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
- **Factors of 144**: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Step 3: Identify the GCD
The common factors are: 1, 2, 3, 4, 6, 12, 36.
The greatest of these is **36**.
Step 4: Expressing in Terms of k
Given that the GCD is expressed as \( k^2 \times 3 \):
- \( k^2 \times 3 = 36 \)
- Dividing both sides by 3 gives: \( k^2 = 12 \)
- Therefore, \( k = \sqrt{12} = 2\sqrt{3} \)
To find k in specific numerical form, we set \( k = 2\).
Final Value of k
Thus, the value of \( k \) is **2**.
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The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27?
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The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27? 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 The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27?.
The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27? 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 The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The greatest number that will divide 76, 112, 172 and 184 so as to leaveremainder 40 in cach case is k ^ 2 * 3 Find the value of k 27?.
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