GCF of 2714/640, 4922/9702
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2714/640, 4922/9702 i.e 46/3104640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2714/640, 4922/9702.
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 2714/640,4922/9702?
Given fractions are 2714/640,4922/9702
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 2714/640,4922/9702, numerators are 2714,4922
Denominators are 640,9702
The GCF of 2714,4922 is 46 .
LCM of 640,9702 is 3104640.
The greatest common factor of 2714/640,4922/9702 = [GCF of 2714,4922]/[LCM of 640,9702]= 46/3104640
Therefore, the GCF of 2714/640,4922/9702 is 46/3104640.
To find the highest common factor of 2714,4922, we have to find the factors of both numbers and list the highest common factor.
The factors of 2714 are 1, 2, 23, 46, 59, 118, 1357, 2714
The factors of 4922 are 1, 2, 23, 46, 107, 214, 2461, 4922
The HCF of 2714,4922 is 46.
Lets's calculate GCF of 2714,4922
| 2 | 2714, 4922 |
| 23 | 1357, 2461 |
| 59, 107 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 2714,4922 By Matching Biggest Common Factor Method
Now, list down the factors of 2714
:1,2,23,46,59,118,1357,2714
Now, list down the factors of 4922
:1,2,23,46,107,214,2461,4922
Greatest Common Factor
We found the factors 2714,4922 . The biggest common factor number is the GCF number.
So the greatest common factor 2714,4922 is 46.
Lets's calculate LCM of 640,9702
| 2 | 640, 9702 |
| 320, 4851 |
∴ So the LCM of the given numbers is 2 x 320 x 4851 = 3104640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/3104640
Therefore, the GCF of Fractions 2714/640,4922/9702 is 46/3104640
Least Common Multiple of 640,9702 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 640,9702 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(640,9702) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(640,9702) x common factors =2 x 1 = 2
LCM(640,9702) = ( 640 × 9702 ) / 2
LCM(640,9702) = 6209280 / 2
LCM(640,9702) = 3104640
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FAQs on GCF of Fractions of 2714/640, 4922/9702
1. What is the HCF of 2714,4922?
The HCF of 2714,4922 is 46
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 2714/640, 4922/9702?
Answer: GCF of Numerators as per given numbers 2714/640, 4922/9702 is
GCF of Numerators i.e. for 2714,4922 is 46
LCM of denominators i.e. for 640,9702 is 3104640.
Thus, GCF of Fractions is 46/3104640.Finally, GCF of Fractions for 2714/640, 4922/9702 is 46/3104640.