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let's have two numbers a and b and a set of primes (pi)

Suppose

a = pa pa+1pa+2...

and b = pb pb+1 pb+2...

If at least one pi in both factorization is in common then the two numbers are not coprime (relatively prime), if none is in common then they are coprime

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βˆ™ 2011-06-08 21:34:20
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Q: How can you use prime factorization of two numbers to determine whether they are relatively prime?
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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.


How can you use prime factorization to determine whether two numbers are relatively prime?

If the prime factorizations contain no factors in common (their GCF is 1), the numbers are relatively prime.


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.


How can you determine from the prime factorization whether the least common multiple of two numbers is the product of the numbers?

If the prime factorizations have no factors in common, the LCM is the product of them.


How can you determine whether the GCF of two numbers is one by looking at their prime factorization?

If there are no prime factors in common, the GCF is 1.


How do you determine Prime Factorization of 35?

By trying out whether you can divide it by different numbers. For one- or two-digit numbers, it is enough to test divisibility by 2, 3, 5, 7.


How can you the prime factorization of two numbers to determine whether they are relatively prime give example?

Example: 36 and 175 2 x 2 x 3 x 3 = 36 5 x 5 x 7 = 175 There are no common prime factors. The GCF is 1. By definition, that makes them relatively prime.


What is the greatest common factor of numbers using prime factorization. then tell whether they are relatively prime?

Example: 4 and 9 2 x 2 = 4 3 x 3 = 9 No common prime factors. The GCF is 1. The numbers are relatively prime.


How can you use the prime factorization to determine whether 35 is a factor of the number?

If the prime factorization contains a 5 and a 7, 35 is a factor.


Is two composite numbers may be relatively prime to each other?

Yes, if they have no common factors. Do the prime factorization for two numbers, and check whether they have, or don't have, common factors. Example: let one of the numbers be 2 x 3, the other 52. Since none of the numbers shares factors with the other one, they are relatively prime.


What is the greatest common factor using prime factorization then tell whether the numbers are relatively prime 98 and 40?

2 x 2 x 2 x 5 = 40 2 x 7 x 7 = 98 The GCF is 2. The numbers are not relatively prime.


How can you determine from the prime factorization whether the least common multiple of two numbers is the product of the number?

If the two numbers have no common prime factors, the LCM will be the product of the numbers.

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