True or false. If two numbers are relatively prime,both numbers are prime. Please help ASAP!!! :( Give an example!!! :)
FALSE
Relatively Prime numbers are numbers whose GCF ( Greatest Common Factor ) is 1.
When two numbers have no common factors other than 1.
In other words there is no value that you could divide them both by exactly (without any remainder).
21 and 22 are relatively prime:
The factors of 21 are 1, 3 , 7 and 21
The factors of 22 are 1, 2 , 11 and 22
The only common factor is 1.
14 and 15
they both are not prime numbers because both have prime factorization
14 = 2 * 7
15 = 3 * 5
6 and 35
6 = 2 * 3
35 = 5 * 7
So they are coprime, also you can see that they have no common factor. which also shows that they are coprime.
Hope this was helpful.
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False! If two numbers are relatively prime, it means that they have no common factors other than 1. However, this does not necessarily mean that both numbers are prime.
Example: The numbers 8 and 9 are relatively prime because their only common factor is 1, but neither of them are prime numbers.
False.
Two numbers are said to be relatively prime if their greatest common divisor (GCD) is 1. This means that there are no positive integers other than 1 that divide both numbers evenly. However, this does not mean that both numbers have to be prime.
For example, let's consider the numbers 15 and 28. The prime factorization of 15 is 3 x 5, and the prime factorization of 28 is 2 x 2 x 7. The greatest common divisor of 15 and 28 is 1, so they are relatively prime. However, neither 15 nor 28 is a prime number.
False. If two numbers are relatively prime, it does not necessarily mean that both numbers are prime. Relatively prime numbers are also known as coprime numbers, which means that their greatest common divisor (GCD) is 1.
To verify whether this statement is true or false, we need to find a counterexample that disproves it. Let's consider the example of 15 and 28. Both numbers are not prime (15 = 3 * 5 and 28 = 2 * 2 * 7), but they are relatively prime because their GCD is 1. Therefore, we have a counterexample that shows that the statement is false.
Remember, to determine if two numbers are relatively prime, we need to calculate their GCD. If the GCD is 1, the numbers are relatively prime, regardless of whether they are prime or composite.