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since 5 and 11 are both prime, their greatest common factor can only be 1.

for any two prime numbers, the answer here is always 1 ... because a Prime number is divisible only by itself and one.

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Q: How can you find the greatest common factor of 5 and 11?
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There is neither a greatest common factor nor common factors of a single number, such as 11, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.The factors of 11 are 1 and 11.The prime factor of 11 is 11; it is a prime number.Examples:The common factors of 11 and 44 are 1 and 11; the greatest common factor is 11.The common factors of 11 and 56 are only 1; the greatest common factor is 1.The common factors of 11 and 71 are only 1; the greatest common factor is 1.The common factors of 11 and 132 are 1 and 11; the greatest common factor is 11.The common factors of 8, 11, and 33 are only 1; the greatest common factor is 1.* because 11 is a prime number there is no common factor just it self !