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course mth 151
8/4 11
Question: `q query 5.3.12 using prime factors find the greatest common factor of 180 and 300.
What is the greatest common factor and how did you use prime factors to find it?
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Your solution:
180=2 ^2 * 3 ^ 2 * 5 and 300=2 ^2 * 3 ^1 * 5^2 they have in commin 2^2, 3 and 5 so this would be 2^2 * 3^1 * 5^1=60 the greatest common factor is 60
3
Ok
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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.
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Your solution:
70 divided by 25 gives us remainder 20 25 by the remainder 20, obtaining remainder 5 divide the previous divisor, which is now 20, by the remainder 5 The remainder of this division is 0 so 5 is the greatest common factor
3
Ok
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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?
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Your solution:
24 = 2*2*2*3, 36 = 2*2*3*3, 48 = 2*2*2*2*3 2*2*2*2 * 3*3 = 144 so the greatest common factor is 144
3
Ok
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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.
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Your solution:
15 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
3
Ok
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