Factoring and Multiples

# What makes the greatest common factor special?

###### Wiki User

###### October 11, 2015 4:23AM

Of all the common factors, it's the largest one.

## Related Questions

###### Asked in Factoring and Multiples

### What is the greatest common factor of 2 and 3?

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.

###### Asked in Factoring and Multiples

### Can two even numbers have a greatest common factor that is an odd number?

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.

###### Asked in Math and Arithmetic, Factoring and Multiples

### Why is 7 the greatest common factor of 28 and 63?

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.

###### Asked in Algebra, Proofs, Factoring and Multiples

### How do you prove that if the greatest common factor of A and B equals 1 and C does not equal 0 then the greatest common factor of AC and BC divides C?

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.)

###### Asked in Math and Arithmetic, Algebra, Factoring and Multiples

### What is the greatest common factor of 15 over 45?

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.

###### Asked in Algebra, Factoring and Multiples

### What has a GCF of 4?

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.

###### Asked in Factoring and Multiples

### What are the common factors and greatest common factor of 180?

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.

###### Asked in Math and Arithmetic

### What is the Greatest common multiple 18 and 20?

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.