GCF of 14/138, 259/153, 780/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/138, 259/153, 780/289 i.e 1/119646 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/138, 259/153, 780/289.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 14/138,259/153,780/289?
Given fractions are 14/138,259/153,780/289
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 14/138,259/153,780/289, numerators are 14,259,780
Denominators are 138,153,289
The GCF of 14,259,780 is 1 .
LCM of 138,153,289 is 119646.
The greatest common factor of 14/138,259/153,780/289 = [GCF of 14,259,780]/[LCM of 138,153,289]= 1/119646
Therefore, the GCF of 14/138,259/153,780/289 is 1/119646.
To find the highest common factor of 14,259,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 259 are 1, 7, 37, 259
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 14,259,780 is 1.
Lets's calculate GCF of 14,259,780
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 14,259,780 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 259
:1,7,37,259
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 14,259,780 . The biggest common factor number is the GCF number.
So the greatest common factor 14,259,780 is 1.
Lets's calculate LCM of 138,153,289
| 3 | 138, 153, 289 |
| 17 | 46, 51, 289 |
| 46, 3, 17 |
∴ So the LCM of the given numbers is 3 x 17 x 46 x 3 x 17 = 119646
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/119646
Therefore, the GCF of Fractions 14/138,259/153,780/289 is 1/119646
Least Common Multiple of 138,153,289 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 138,153,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(138,153,289) = 1
common factors(in case of two or more numbers have common factors) = 51
GCF(138,153,289) x common factors =1 x 51 = 51
LCM(138,153,289) = ( 138 × 153 × 289 ) / 51
LCM(138,153,289) = 6101946 / 51
LCM(138,153,289) = 119646
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FAQs on GCF of Fractions of 14/138, 259/153, 780/289
1. What is the HCF of 14,259,780?
The HCF of 14,259,780 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 14/138, 259/153, 780/289?
Answer: GCF of Numerators as per given numbers 14/138, 259/153, 780/289 is
GCF of Numerators i.e. for 14,259,780 is 1
LCM of denominators i.e. for 138,153,289 is 119646.
Thus, GCF of Fractions is 1/119646.Finally, GCF of Fractions for 14/138, 259/153, 780/289 is 1/119646.