#$&* course mth151 12/17/14 1 If your solution to stated problem does not match the given solution, you should self-critique per instructions
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Given Solution: `a** The prime factorizations are 180=2 ^2 * 3 ^ 2 * 5 and 300=2 ^2 * 3 ^1 * 5^2. They have in commin 2^2, 3 and 5, and no higher power of any of these factors. Since 2^2 * 3^1 * 5^1=60 the greatest common factor is 60. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q query 5.3.24 Euclidean algorithm to find GCF(25,70) Show how you used the Euclidean algorithm to find the greatest common factor of the two numbers. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: we have to divide the largest number,70, by the smaller, 25. when we get the remainder of this, we divide the small number, 25, by the remainder. then we divide the second remainder by the first remainder. I know I explained this badly but here's what you do... 70/25=2 remainder 20 25/20=1 remainder 5 20/5=5 remainder 0 since 5 was the last remainder, then that is the greatest common factor confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** To apply the Euclidean algorithm we divide the larger number by the smaller, obtaining a remainder. We then divide the remainder by the divisor and repeat this process until we get 0 remainder. The greatest common divisor is the last divisor. In this case 70 divided by 25 gives us remainder 20. Then we divide the previous divisor 25 by the remainder 20, obtaining remainder 5. Then we divide the previous divisor, which is now 20, by the remainder 5. The remainder of this division is 0. So the last divisor, which is 5, is the greatest common factor. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q query 5.3.36 LCM of 24, 36, 48 How did you use the prime factors of the given numbers to find their greatest common factor? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 24 2*12 2*3*4 2*2*2*3 36 2*18 2*2*9 2*2*3*3 48 2*24 2*2*12 2*2*4*3 2*2*2*2*3 use only factors that are common to all the numbers 2*2*3=12 is the greatest common factor now we have to combine the prime factorizations so that the new has all the factors in it, without duplicating factors 2*2*2*2*3*3=144 is the least common multiple confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The prime factorizations are 24 = 2*2*2*3, 36 = 2*2*3*3, 48 = 2*2*2*2*3. The smallest number that includes all these factors has four 2's and two 3's. 2*2*2*2 * 3*3 = 144. So 144 is the GCF. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q query 5.3.48 GCF of 48, 315, 450 Show how you used the Euclidean algorithm to find the greatest common factor of the three given numbers. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 315 and 48 315/48= remainder 27 48/27= remainder 21 27/21= remainder 6 21/6= remainder 3 6/3= remainder 0 since 3 was the last remainder, 3 is the greatest common factor confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** Applying the Euclidean Algorithm to 315 and 48: 315 divided by 48 gives us remainder 27. 48 divided by 27 gives us remainder 21. 27 divided by 21 gives us remainder 3. 6 divided by 3 gives us remainder 0. The last divisor is 3, which is therefore the GCF of 315 and 48. The GCF of the three numbers is therefore the GCF of 450 and 3, which is found by first dividing 450 by 3, which gives us remainder 0. So the last divisor is 3, which is therefore the GCF of the three numbers. ** Query Add comments on any surprises or insights you experienced as a result of this assignment. already knew most of this so it was no surprise to me " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q query 5.3.48 GCF of 48, 315, 450 Show how you used the Euclidean algorithm to find the greatest common factor of the three given numbers. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 315 and 48 315/48= remainder 27 48/27= remainder 21 27/21= remainder 6 21/6= remainder 3 6/3= remainder 0 since 3 was the last remainder, 3 is the greatest common factor confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** Applying the Euclidean Algorithm to 315 and 48: 315 divided by 48 gives us remainder 27. 48 divided by 27 gives us remainder 21. 27 divided by 21 gives us remainder 3. 6 divided by 3 gives us remainder 0. The last divisor is 3, which is therefore the GCF of 315 and 48. The GCF of the three numbers is therefore the GCF of 450 and 3, which is found by first dividing 450 by 3, which gives us remainder 0. So the last divisor is 3, which is therefore the GCF of the three numbers. ** Query Add comments on any surprises or insights you experienced as a result of this assignment. already knew most of this so it was no surprise to me " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!