GCF of 7714/970, 3952/2014
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7714/970, 3952/2014 i.e 38/976790 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7714/970, 3952/2014.
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 7714/970,3952/2014?
Given fractions are 7714/970,3952/2014
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 7714/970,3952/2014, numerators are 7714,3952
Denominators are 970,2014
The GCF of 7714,3952 is 38 .
LCM of 970,2014 is 976790.
The greatest common factor of 7714/970,3952/2014 = [GCF of 7714,3952]/[LCM of 970,2014]= 38/976790
Therefore, the GCF of 7714/970,3952/2014 is 38/976790.
To find the highest common factor of 7714,3952, we have to find the factors of both numbers and list the highest common factor.
The factors of 7714 are 1, 2, 7, 14, 19, 29, 38, 58, 133, 203, 266, 406, 551, 1102, 3857, 7714
The factors of 3952 are 1, 2, 4, 8, 13, 16, 19, 26, 38, 52, 76, 104, 152, 208, 247, 304, 494, 988, 1976, 3952
The HCF of 7714,3952 is 38.
Lets's calculate GCF of 7714,3952
| 2 | 7714, 3952 |
| 19 | 3857, 1976 |
| 203, 104 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 7714,3952 By Matching Biggest Common Factor Method
Now, list down the factors of 7714
:1,2,7,14,19,29,38,58,133,203,266,406,551,1102,3857,7714
Now, list down the factors of 3952
:1,2,4,8,13,16,19,26,38,52,76,104,152,208,247,304,494,988,1976,3952
Greatest Common Factor
We found the factors 7714,3952 . The biggest common factor number is the GCF number.
So the greatest common factor 7714,3952 is 38.
Lets's calculate LCM of 970,2014
| 2 | 970, 2014 |
| 485, 1007 |
∴ So the LCM of the given numbers is 2 x 485 x 1007 = 976790
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/976790
Therefore, the GCF of Fractions 7714/970,3952/2014 is 38/976790
Least Common Multiple of 970,2014 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 970,2014 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(970,2014) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(970,2014) x common factors =2 x 1 = 2
LCM(970,2014) = ( 970 × 2014 ) / 2
LCM(970,2014) = 1953580 / 2
LCM(970,2014) = 976790
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FAQs on GCF of Fractions of 7714/970, 3952/2014
1. What is the HCF of 7714,3952?
The HCF of 7714,3952 is 38
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 7714/970, 3952/2014?
Answer: GCF of Numerators as per given numbers 7714/970, 3952/2014 is
GCF of Numerators i.e. for 7714,3952 is 38
LCM of denominators i.e. for 970,2014 is 976790.
Thus, GCF of Fractions is 38/976790.Finally, GCF of Fractions for 7714/970, 3952/2014 is 38/976790.