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

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

Mathematics
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35=3*175-2*245
s=3, t=-2 for one solution
what do you mean for one solution?

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there are infinite possibilities for s and t, i'm just giving you one possiblity
oh ok
but what is GCD of (175,245)?
35
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
hey pizzapi, would you be able to show me the step of how you got s=3 and t= -2
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)
yea i am having really tough time understanding euclidean algorithm
would you help me understand this algorithm

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