GCF of 137/198, 813/693
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 137/198, 813/693 i.e 1/1386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 137/198, 813/693.
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 137/198,813/693?
Given fractions are 137/198,813/693
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 137/198,813/693, numerators are 137,813
Denominators are 198,693
The GCF of 137,813 is 1 .
LCM of 198,693 is 1386.
The greatest common factor of 137/198,813/693 = [GCF of 137,813]/[LCM of 198,693]= 1/1386
Therefore, the GCF of 137/198,813/693 is 1/1386.
To find the highest common factor of 137,813, we have to find the factors of both numbers and list the highest common factor.
The factors of 137 are 1, 137
The factors of 813 are 1, 3, 271, 813
The HCF of 137,813 is 1.
Lets's calculate GCF of 137,813
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 137,813 By Matching Biggest Common Factor Method
Now, list down the factors of 137
:1,137
Now, list down the factors of 813
:1,3,271,813
Greatest Common Factor
We found the factors 137,813 . The biggest common factor number is the GCF number.
So the greatest common factor 137,813 is 1.
Lets's calculate LCM of 198,693
| 3 | 198, 693 |
| 3 | 66, 231 |
| 11 | 22, 77 |
| 2, 7 |
∴ So the LCM of the given numbers is 3 x 3 x 11 x 2 x 7 = 1386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1386
Therefore, the GCF of Fractions 137/198,813/693 is 1/1386
Least Common Multiple of 198,693 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 198,693 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,693) = 99
common factors(in case of two or more numbers have common factors) = 1
GCF(198,693) x common factors =99 x 1 = 99
LCM(198,693) = ( 198 × 693 ) / 99
LCM(198,693) = 137214 / 99
LCM(198,693) = 1386
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FAQs on GCF of Fractions of 137/198, 813/693
1. What is the HCF of 137,813?
The HCF of 137,813 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 137/198, 813/693?
Answer: GCF of Numerators as per given numbers 137/198, 813/693 is
GCF of Numerators i.e. for 137,813 is 1
LCM of denominators i.e. for 198,693 is 1386.
Thus, GCF of Fractions is 1/1386.Finally, GCF of Fractions for 137/198, 813/693 is 1/1386.