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The prime factorization of 560 is: 2, 5, and 7
If your numbers have no prime factors in common, they are relatively prime.
Use the disibility rules
Once your prime factorization is complete and you discover that there are no numbers in common, the GCF is one and the numbers are declared to be relatively prime.
No, 3x5x4 is not a prime factorization of 60. A prime factorization of 60 would consist of only prime numbers. The prime factorization of 60 is 2x2x3x5.