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138 = 2 X 3 X 23 and 102 = 2 X 3 X 17. 17 and 23 are both prime numbers; therefore, the greatest common divisor of the two specified numbers is 2 X 3 = 6.

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Q: Greatest common divisor of 138 and 102?
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What is the greatest common factor of 102 and 138?

Greatest common factor of 102 and 138 is 2.


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What is the greatest common factor of 115 and 138?

Expressing each number as the product of their prime factors is one of the methods of finding greatest common factor.115 = 5 x 23225 = 3 x 3 x 5 x 5As 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+ rApplying the theorem to 225 and 115 we get.Step I225 = 115 x 1 + 110Now the remainder and divisor in step I becomes divisor and dividend for step II.Step II115 = 110 x 1 + 5Step III110 = 5 x 22 + 0When 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).