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To have a gcf of 18 they must have one factor of 18 in common and no other factor, ie the second factor of the numbers must be relatively prime.

The multiples of 18 between 200 and 300 are:

12 x 18 = 216

13 x 18 = 234

14 x 18 = 252

15 x 18 = 270

16 x 18 = 288

12 is relatively prime to 13

13 is relatively prime to 14, 15 & 16

14 is relatively prime to 15

15 is relatively prime to 16

(Pairs of numbers are being considered, so as 12 is relatively prime to 13, 13 is also relatively prime to 12 and thus is only listed when the numbers increase, ie under 12 and not under 13.)

Thus the pairs:

216 & 234

234 & 252

234 & 270

234 & 288

252 & 270

270 & 288

all have a gcf of 18.

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13y ago
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Q: What pair of numbers between 200 and 300 has a gcf of 18?
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