GCF of 70/656, 5194/3124
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/656, 5194/3124 i.e 14/512336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/656, 5194/3124.
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 70/656,5194/3124?
Given fractions are 70/656,5194/3124
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 70/656,5194/3124, numerators are 70,5194
Denominators are 656,3124
The GCF of 70,5194 is 14 .
LCM of 656,3124 is 512336.
The greatest common factor of 70/656,5194/3124 = [GCF of 70,5194]/[LCM of 656,3124]= 14/512336
Therefore, the GCF of 70/656,5194/3124 is 14/512336.
To find the highest common factor of 70,5194, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 5194 are 1, 2, 7, 14, 49, 53, 98, 106, 371, 742, 2597, 5194
The HCF of 70,5194 is 14.
Lets's calculate GCF of 70,5194
| 2 | 70, 5194 |
| 7 | 35, 2597 |
| 5, 371 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 70,5194 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 5194
:1,2,7,14,49,53,98,106,371,742,2597,5194
Greatest Common Factor
We found the factors 70,5194 . The biggest common factor number is the GCF number.
So the greatest common factor 70,5194 is 14.
Lets's calculate LCM of 656,3124
| 2 | 656, 3124 |
| 2 | 328, 1562 |
| 164, 781 |
∴ So the LCM of the given numbers is 2 x 2 x 164 x 781 = 512336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/512336
Therefore, the GCF of Fractions 70/656,5194/3124 is 14/512336
Least Common Multiple of 656,3124 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 656,3124 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(656,3124) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(656,3124) x common factors =4 x 1 = 4
LCM(656,3124) = ( 656 × 3124 ) / 4
LCM(656,3124) = 2049344 / 4
LCM(656,3124) = 512336
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FAQs on GCF of Fractions of 70/656, 5194/3124
1. What is the HCF of 70,5194?
The HCF of 70,5194 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 70/656, 5194/3124?
Answer: GCF of Numerators as per given numbers 70/656, 5194/3124 is
GCF of Numerators i.e. for 70,5194 is 14
LCM of denominators i.e. for 656,3124 is 512336.
Thus, GCF of Fractions is 14/512336.Finally, GCF of Fractions for 70/656, 5194/3124 is 14/512336.