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All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
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How can you use prime factorization to determine if two numbers are relatively prime?
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.
Explanin How do you determine the prime factorzation of 56?
the prime factorization of 56 is a prime number that are only divisible by twounique factors.
How can you use the prime factorization of two numbers to determine whether they are relative prime?
If the prime factorizations have no prime factors in common, the numbers are relatively prime.
Why would you determine the prime factorization of only composite numbers?
Because the prime decomposition of primes is trivial and pointless.
How can you use the prime factorization of two numbers to determine whether they are relatively prime?
Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.
