Prime factors are part of prime factorizations. Prime factorizations help in finding the GCF and LCM of integers. Finding the GCF helps in reducing fractions. Finding the LCM helps in adding and subtracting unlike fractions. Carpenters do this. Chefs do this. It's entirely possible you will have no need of this, but it's better to know something and not need to use it then not know something you need to use. If you have children of your own, you can help them with their math homework.
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Yes they are most likely used in your everyday life- even if you don't realize it. Computers use prime numbers in the encryption techniques. If you log in to a website in secure mode, most likely prime numbers are being used, but you don't even know about it.
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Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.
If your numbers have no prime factors in common, they are relatively prime.
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