GCF of 742/198, 294/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 742/198, 294/676 i.e 14/66924 easily. The following is the detailed procedure to determine the greatest common factor of fractions 742/198, 294/676.
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 742/198,294/676?
Given fractions are 742/198,294/676
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 742/198,294/676, numerators are 742,294
Denominators are 198,676
The GCF of 742,294 is 14 .
LCM of 198,676 is 66924.
The greatest common factor of 742/198,294/676 = [GCF of 742,294]/[LCM of 198,676]= 14/66924
Therefore, the GCF of 742/198,294/676 is 14/66924.
To find the highest common factor of 742,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 742 are 1, 2, 7, 14, 53, 106, 371, 742
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 742,294 is 14.
Lets's calculate GCF of 742,294
| 2 | 742, 294 |
| 7 | 371, 147 |
| 53, 21 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 742,294 By Matching Biggest Common Factor Method
Now, list down the factors of 742
:1,2,7,14,53,106,371,742
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 742,294 . The biggest common factor number is the GCF number.
So the greatest common factor 742,294 is 14.
Lets's calculate LCM of 198,676
| 2 | 198, 676 |
| 99, 338 |
∴ So the LCM of the given numbers is 2 x 99 x 338 = 66924
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/66924
Therefore, the GCF of Fractions 742/198,294/676 is 14/66924
Least Common Multiple of 198,676 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 198,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,676) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(198,676) x common factors =2 x 1 = 2
LCM(198,676) = ( 198 × 676 ) / 2
LCM(198,676) = 133848 / 2
LCM(198,676) = 66924
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 742/198, 294/676
1. What is the HCF of 742,294?
The HCF of 742,294 is 14
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 742/198, 294/676?
Answer: GCF of Numerators as per given numbers 742/198, 294/676 is
GCF of Numerators i.e. for 742,294 is 14
LCM of denominators i.e. for 198,676 is 66924.
Thus, GCF of Fractions is 14/66924.Finally, GCF of Fractions for 742/198, 294/676 is 14/66924.