GCF of 2770/208, 2208/724
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2770/208, 2208/724 i.e 2/37648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2770/208, 2208/724.
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 2770/208,2208/724?
Given fractions are 2770/208,2208/724
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 2770/208,2208/724, numerators are 2770,2208
Denominators are 208,724
The GCF of 2770,2208 is 2 .
LCM of 208,724 is 37648.
The greatest common factor of 2770/208,2208/724 = [GCF of 2770,2208]/[LCM of 208,724]= 2/37648
Therefore, the GCF of 2770/208,2208/724 is 2/37648.
To find the highest common factor of 2770,2208, we have to find the factors of both numbers and list the highest common factor.
The factors of 2770 are 1, 2, 5, 10, 277, 554, 1385, 2770
The factors of 2208 are 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208
The HCF of 2770,2208 is 2.
Lets's calculate GCF of 2770,2208
| 2 | 2770, 2208 |
| 1385, 1104 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2770,2208 By Matching Biggest Common Factor Method
Now, list down the factors of 2770
:1,2,5,10,277,554,1385,2770
Now, list down the factors of 2208
:1,2,3,4,6,8,12,16,23,24,32,46,48,69,92,96,138,184,276,368,552,736,1104,2208
Greatest Common Factor
We found the factors 2770,2208 . The biggest common factor number is the GCF number.
So the greatest common factor 2770,2208 is 2.
Lets's calculate LCM of 208,724
| 2 | 208, 724 |
| 2 | 104, 362 |
| 52, 181 |
∴ So the LCM of the given numbers is 2 x 2 x 52 x 181 = 37648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/37648
Therefore, the GCF of Fractions 2770/208,2208/724 is 2/37648
Least Common Multiple of 208,724 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 208,724 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,724) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(208,724) x common factors =4 x 1 = 4
LCM(208,724) = ( 208 × 724 ) / 4
LCM(208,724) = 150592 / 4
LCM(208,724) = 37648
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FAQs on GCF of Fractions of 2770/208, 2208/724
1. What is the HCF of 2770,2208?
The HCF of 2770,2208 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 2770/208, 2208/724?
Answer: GCF of Numerators as per given numbers 2770/208, 2208/724 is
GCF of Numerators i.e. for 2770,2208 is 2
LCM of denominators i.e. for 208,724 is 37648.
Thus, GCF of Fractions is 2/37648.Finally, GCF of Fractions for 2770/208, 2208/724 is 2/37648.