GCF of 274/298, 7254/178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 274/298, 7254/178 i.e 2/26522 easily. The following is the detailed procedure to determine the greatest common factor of fractions 274/298, 7254/178.
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 274/298,7254/178?
Given fractions are 274/298,7254/178
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 274/298,7254/178, numerators are 274,7254
Denominators are 298,178
The GCF of 274,7254 is 2 .
LCM of 298,178 is 26522.
The greatest common factor of 274/298,7254/178 = [GCF of 274,7254]/[LCM of 298,178]= 2/26522
Therefore, the GCF of 274/298,7254/178 is 2/26522.
To find the highest common factor of 274,7254, we have to find the factors of both numbers and list the highest common factor.
The factors of 274 are 1, 2, 137, 274
The factors of 7254 are 1, 2, 3, 6, 9, 13, 18, 26, 31, 39, 62, 78, 93, 117, 186, 234, 279, 403, 558, 806, 1209, 2418, 3627, 7254
The HCF of 274,7254 is 2.
Lets's calculate GCF of 274,7254
| 2 | 274, 7254 |
| 137, 3627 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 274,7254 By Matching Biggest Common Factor Method
Now, list down the factors of 274
:1,2,137,274
Now, list down the factors of 7254
:1,2,3,6,9,13,18,26,31,39,62,78,93,117,186,234,279,403,558,806,1209,2418,3627,7254
Greatest Common Factor
We found the factors 274,7254 . The biggest common factor number is the GCF number.
So the greatest common factor 274,7254 is 2.
Lets's calculate LCM of 298,178
| 2 | 298, 178 |
| 149, 89 |
∴ So the LCM of the given numbers is 2 x 149 x 89 = 26522
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/26522
Therefore, the GCF of Fractions 274/298,7254/178 is 2/26522
Least Common Multiple of 298,178 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 298,178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(298,178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(298,178) x common factors =2 x 1 = 2
LCM(298,178) = ( 298 × 178 ) / 2
LCM(298,178) = 53044 / 2
LCM(298,178) = 26522
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FAQs on GCF of Fractions of 274/298, 7254/178
1. What is the HCF of 274,7254?
The HCF of 274,7254 is 2
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 274/298, 7254/178?
Answer: GCF of Numerators as per given numbers 274/298, 7254/178 is
GCF of Numerators i.e. for 274,7254 is 2
LCM of denominators i.e. for 298,178 is 26522.
Thus, GCF of Fractions is 2/26522.Finally, GCF of Fractions for 274/298, 7254/178 is 2/26522.