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16 Sep 2014, 00:50
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What is the sum of all common positive factors of 48 and 36?
A. 22
B. 24
C. 26
D. 27
E. 28
A. 22
B. 24
C. 26
D. 27
E. 28
16 Sep 2014, 00:50
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Official Solution:
What is the sum of all common positive factors of 48 and 36?
A. 22
B. 24
C. 26
D. 27
E. 28
Step 1: Find the greatest common divisor (GCD) of 48 and 36.
• Why start with the GCD? The GCD of two numbers is the largest number that divides both of them without leaving a remainder. As such, all the positive factors of the GCD will also be common factors of the two numbers.
The GCD of \(48 = 2^4*3\) and \(36 = 2^2*3^2\) is \(2^2*3 = 12\).
Step 2: Find the positive factors of 12.
The positive factors are: 1, 2, 3, 4, 6, and 12.
Step 3: Sum up the factors.
\(1 + 2 + 3 + 4 + 6 + 12 = 28\).
Therefore, the sum of all common positive factors of 48 and 36 is 28.
Answer: E
What is the sum of all common positive factors of 48 and 36?
A. 22
B. 24
C. 26
D. 27
E. 28
Step 1: Find the greatest common divisor (GCD) of 48 and 36.
• Why start with the GCD? The GCD of two numbers is the largest number that divides both of them without leaving a remainder. As such, all the positive factors of the GCD will also be common factors of the two numbers.
The GCD of \(48 = 2^4*3\) and \(36 = 2^2*3^2\) is \(2^2*3 = 12\).
Step 2: Find the positive factors of 12.
The positive factors are: 1, 2, 3, 4, 6, and 12.
Step 3: Sum up the factors.
\(1 + 2 + 3 + 4 + 6 + 12 = 28\).
Therefore, the sum of all common positive factors of 48 and 36 is 28.
Answer: E
General Discussion
06 Sep 2023, 10:53
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
