What is the greatest common factor of 225 and 825?

Answer 1

For small numbers which we can factorize easily, it is practical to use prime factorizations to find the greatest common factor. For larger numbers, however, this is not always practical. So instead we use the Euclidean Algorithm, as follows. (Here, * means multiply.)

330495 = 400 * 825 + 495

825 = 1 * 495 + 330

495 = 1 * 330 + 165

330 = 2 * 165 + 0

At each step, we divide one number by the other and get a remainder. (So when 330495 is divided by 825 the remainder is 495, etc). So we get the sequence 330495 , 825 , 495 , 330 , 165 , 0.

Every common factor of 330495 and 825 is also a factor of 495, and every common factor of 825 and 495 is also a factor of 330495. Therefore the common factors of 330495 and 825 are precisely the common factors of 825 and 495. Similarly, the common factors of 825 and 495 are precisely the common factors of 495 and 330; and the common factors of 495 and 330 are precisely the common factors of 330 and 165; and these are precisely the factors of 165. In short, the common factors of the original two numbers are the factors of 165 (including 165 itself) and no others.

Answer 2

There cannot be a greatest common factor (GCF) of just one number. To be common there need to be at least two numbers. If you find all the factors of two or more numbers, and you find some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.

Answer 3

The greatest common factor of 225 and 825 is 75.

Answer 4

Unless I overlooked something 33 is the greatest common factor of 330 and 429

Answer 5

The GCF/HCF of 330 and 945 is 15.

Answer 6

The GCF is 75.