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anonymous

  • 4 years ago

find the GCD (175,245) and write it in the form 175s + t245 with integers s,t

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  1. anonymous
    • 4 years ago
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    35=3*175-2*245

  2. anonymous
    • 4 years ago
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    s=3, t=-2 for one solution

  3. anonymous
    • 4 years ago
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    what do you mean for one solution?

  4. anonymous
    • 4 years ago
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    there are infinite possibilities for s and t, i'm just giving you one possiblity

  5. anonymous
    • 4 years ago
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    oh ok

  6. anonymous
    • 4 years ago
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    but what is GCD of (175,245)?

  7. anonymous
    • 4 years ago
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    35

  8. Edchau3
    • 4 years ago
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    To find the GCD (Greatest Common Denominator), first reduce the two numbers to their prime factors: 175 = 7 * 5 * 5 245 = 7 * 7 * 5 The two numbers have one 7 and one 5 in common, so the GCD is 7 * 5 = 35 If the top number had been 1,225, and the bottom number remained the same, the factors would be: 1,225 = 7 * 7 * 5 * 5 245 = 7 * 7 * 5 The two numbers now have two 7’s and one 5 in common, so the GCD is 7 * 7 * 5 = 245 If the top number had stayed the same and the bottom number had been 1,225, the factors would be 175 = 7 * 5 * 5 1,225 = 7 * 7 * 5 * 5 The two numbers now have one 7 and two 5’s in common, so the GCD is 7 * 5 * 5 = 175

  9. anonymous
    • 4 years ago
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    hey pizzapi, would you be able to show me the step of how you got s=3 and t= -2

  10. anonymous
    • 4 years ago
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    oh, I did it by inspection but you could use the euclidean algorithm to do it 245=(1)(175)+70 175=2(70)+35 70=2(35) Thus 35=175-2(70) 35=175-2(245-175) 35=3(175)-2(245)

  11. anonymous
    • 4 years ago
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    yea i am having really tough time understanding euclidean algorithm

  12. anonymous
    • 4 years ago
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    would you help me understand this algorithm

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