GCF of 208/77, 374/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 208/77, 374/214 i.e 2/16478 easily. The following is the detailed procedure to determine the greatest common factor of fractions 208/77, 374/214.
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 208/77,374/214?
Given fractions are 208/77,374/214
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 208/77,374/214, numerators are 208,374
Denominators are 77,214
The GCF of 208,374 is 2 .
LCM of 77,214 is 16478.
The greatest common factor of 208/77,374/214 = [GCF of 208,374]/[LCM of 77,214]= 2/16478
Therefore, the GCF of 208/77,374/214 is 2/16478.
To find the highest common factor of 208,374, we have to find the factors of both numbers and list the highest common factor.
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 374 are 1, 2, 11, 17, 22, 34, 187, 374
The HCF of 208,374 is 2.
Lets's calculate GCF of 208,374
| 2 | 208, 374 |
| 104, 187 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 208,374 By Matching Biggest Common Factor Method
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 374
:1,2,11,17,22,34,187,374
Greatest Common Factor
We found the factors 208,374 . The biggest common factor number is the GCF number.
So the greatest common factor 208,374 is 2.
Lets's calculate LCM of 77,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 16478
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16478
Therefore, the GCF of Fractions 208/77,374/214 is 2/16478
Least Common Multiple of 77,214 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 77,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,214) x common factors =1 x 1 = 1
LCM(77,214) = ( 77 × 214 ) / 1
LCM(77,214) = 16478 / 1
LCM(77,214) = 16478
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FAQs on GCF of Fractions of 208/77, 374/214
1. What is the HCF of 208,374?
The HCF of 208,374 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 208/77, 374/214?
Answer: GCF of Numerators as per given numbers 208/77, 374/214 is
GCF of Numerators i.e. for 208,374 is 2
LCM of denominators i.e. for 77,214 is 16478.
Thus, GCF of Fractions is 2/16478.Finally, GCF of Fractions for 208/77, 374/214 is 2/16478.