Q: What makes the greatest common factor special?

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These numbers are co-prime, ie they have no common factor other than 1 which makes their GCF 1.

Two (or more) integers have a common factor - e.g., the greatest common factor of 173 and 100 is 1, or the greatest common factor of 173 and 519 is 173. The question makes no sense with one number. 173 is a prime, by the way.

What makes a greatest common factor "common" is comparing at least two terms and finding something common between them.

By noticing that 100 is a factor of 200. That automatically makes it the GCF.

72 is a single number. Common refers to two or more objects. In the case of common factors, we need two or more numbers to have a common factor. The common or greatest common factor of 72 makes no sense.

i have no clue. i want to know. it makes no sence whatsoever

Actually, both can be true, but the answer your teacher is probably looking for is "greatest."

The least common factor of any set of integers is 1.

The greatest common factor of 2 and 3 is 1. This is because 2 and 3 are prime numbers, that is, they only have themselves and one as factors. NOTE: Any time that one of the numbers is a prime number and the other is not a multiple of that prime number, the greatest common factor is 1. Another way to approach this, especially with larger numbers (but this makes a good example) is to look at the difference between 2 and 3, which is 1. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. If the difference is 1, the greatest common factor is 1.

It used to be called "reducing to lowest terms"; nowadays I think it's called "writing the fractionin simplest form".And by the way ... you don't divide the 'fraction' by the greatest commen factor. You divide the numeratorand denominator separately by their greatest commen factor. It makes a big difference.

The GCF is 1 which makes those numbers relatively prime.

No. Because both numbers are even, they each have 2 as a factor. Even if they have a larger factor in common, it will be a multiple of 2, so the greatest common factor will be an even number.Yes. Two even numbers are each divisible by 2. The GCF must therefore always have two as one of its factors; this makes it even.

7 is a factor of 28 because 4 x 7 equals 28. 7 is a factor of 63 because 9 x 7 = 63. That makes 7 a common factor of 28 and 63. The factors of 28 that are larger than 7 are 14 and 28. The factors of 63 that are larger than 7 are 9, 21 and 63. Since none of those numbers are the same, that makes 7 the greatest common factor of 28 and 63.

the greatest common factors of what? The question makes no sense as it stands.

If the greatest common factor/divisor of A and B is 1 then they are coprime - they do not share any prime factors. Multiplying both through by C means, obviously, that each number now divides by C. In fact, C is their greatest common divisor, since AC and BC do not have further common factors after C is taken out. Hence the GCF of AC and BC is not merely a factor of C - it is C. (The question makes sense only if A, B and C are integers.)

It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! That number is 15/45, a fraction that is smaller than 1. The concept of factors makes sense in context of whole numbers since otherwise every non-zero number is a factor of every number.

44

The GCF refers to the relationship between at least two positive integers.

The Greatest Common Factor of four is four. This is because the highest number that can be multiplied by another number to make four (the factor), is four. When four is multiplied by one, it makes four. Even though two multiplied by two makes four, it is not the highest/greatest number that can be multiplied to make four.

There is not a greatest common factor of 180 because there cannot be a greatest common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. The prime factors of 180 are 2, 2, 3, 3, and 5. common means two or more numbers, so this makes no sense.

And the GCF is 6. That makes the difference between the two 30.

It means have you got the eXtra bit or factor which makes you special.

The GCF for 12, 18 and 26 is 2.The prime factorization of 12 is 2^2 x 3The prime factorization of 18 is 2 x 3^2The prime factorization of 26 is 2 x 13The GCF is 2.The GCF is 2.

GCF(23, 69, 92) = 23. Listing 69 twice makes no difference.

The Answer:The greatest common multiple would be infinity, since multiplying both an infinite amount of times approach infinity. Greatest Common Divisor:This should yield 2 as the largest common factor.Least Common Multiple:Since 2 is the GCD, dividing 18 by 2 makes 9, 20 by 2 = 10, and multiplying the values together yields 180.

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