What is the greatest common factor of 115 and 138?

Answer 1

Expressing each number as the product of their prime factors is one of the methods of finding greatest common factor.

115 = 5 x 23

225 = 3 x 3 x 5 x 5

As it can be seen only one 5 is common so GCF is 1.

Another method which can be employed is long division method.

Long division method is based on Euclid's Division Lemma.

Lemma is: For two integers a and b(a>b; b ≠ 0) there exist two integers q and r such that a = bq+ r

Applying the theorem to 225 and 115 we get.

Step I

225 = 115 x 1 + 110

Now the remainder and divisor in step I becomes divisor and dividend for step II.

Step II

115 = 110 x 1 + 5

Step III

110 = 5 x 22 + 0

When the remainder is 0 then the last divisor is the required GCF, which in this case is 5.

The main reason for taking remainder and divisor for next step as divisor and dividend is that factors common between 225 and 115 are also common between 110(r) and 115(q).

Answer 2

The greatest common factor of 115 and 138 is 23.

Answer 3

The greatest common factor of 138 , 299 , 92 , 115 and 253 = 23

Answer 4

The GCF of 138 and 345 is 69

Answer 5

The GCF is 23.