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5, 10 15, 20 500, 505
Here are pairs of numbers with 6 as their greatest common factor: 6, 18 12, 30 120, 126 306, 318 6 and 12
Two pairs of numbers with a GCF of 8 and an LCM of 360 are 360 and 8 and 72 and 40
There is an infinity of pairs of numbers with a GCF of 4. If p and P are two distinct primes, then 4p and 4P are such a pair. There are other ways to construct such pairs, but one infinity should suffice.
The factor pairs of 8 are (8,1)(4,2) The GCF requires at least two numbers.