#$&* course Mth 151 026. `query 26
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Given Solution: `a** The prime factorizations are 180=2 ^2 * 3 ^ 2 * 5 and 300=2 ^2 * 3 ^1 * 5^2. They have in commin 2^2, 3 and 5, and no higher power of any of these factors. Since 2^2 * 3^1 * 5^1=60 the greatest common factor is 60. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q query 5.3.24 Euclidean algorithm to find GCF(25,70) Show how you used the Euclidean algorithm to find the greatest common factor of the two numbers. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: When you divide 70 by 25, you get a remainder of 20 Then you divide 25 by 20, giving you a remainder of 5 Then you divide 20 by 5, giving you a remainder of 0 Since 5 was the last number divided in to give a remainder of 0, it is the GCF confidence rating #$&*: 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: 3 ********************************************* 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 = 2^3 * 3 36 = 2^2 * 3^2 48 = 2^4 * 3 The greatest exponents among the numbers are 2^4 and 3^2 2^4 * 3^2 = 144 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The prime factorizations are 24 = 2*2*2*3, 36 = 2*2*3*3, 48 = 2*2*2*2*3. The smallest number that includes all these factors has four 2's and two 3's. 2*2*2*2 * 3*3 = 144. So 144 is the GCF. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q query 5.3.48 GCF of 48, 315, 450 Show how you used the Euclidean algorithm to find the greatest common factor of the three given numbers. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: First you take 315 and 48 315/48 gives you a remainder of 27 48/27 gives you a remainder of 21 27/21 gives you a remainder of 3 21/3 leaves with you no remainder making 3 the GCF of 315 and 48 Then you take 450 and 3 450/3 leaves you no remainder so the overall GCF of 48, 315, and 450 is 3 confidence rating #$&*: 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. In the above solution, it shows there's a 6 divided by a 3. Where did that six come from??? That number should be 21 divided by 3." 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: First you take 315 and 48 315/48 gives you a remainder of 27 48/27 gives you a remainder of 21 27/21 gives you a remainder of 3 21/3 leaves with you no remainder making 3 the GCF of 315 and 48 Then you take 450 and 3 450/3 leaves you no remainder so the overall GCF of 48, 315, and 450 is 3 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. In the above solution, it shows there's a 6 divided by a 3. Where did that six come from??? That number should be 21 divided by 3." Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!