GCF of 6314/974, 5740/5639
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6314/974, 5740/5639 i.e 574/5492386 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6314/974, 5740/5639.
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 6314/974,5740/5639?
Given fractions are 6314/974,5740/5639
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 6314/974,5740/5639, numerators are 6314,5740
Denominators are 974,5639
The GCF of 6314,5740 is 574 .
LCM of 974,5639 is 5492386.
The greatest common factor of 6314/974,5740/5639 = [GCF of 6314,5740]/[LCM of 974,5639]= 574/5492386
Therefore, the GCF of 6314/974,5740/5639 is 574/5492386.
To find the highest common factor of 6314,5740, we have to find the factors of both numbers and list the highest common factor.
The factors of 6314 are 1, 2, 7, 11, 14, 22, 41, 77, 82, 154, 287, 451, 574, 902, 3157, 6314
The factors of 5740 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 41, 70, 82, 140, 164, 205, 287, 410, 574, 820, 1148, 1435, 2870, 5740
The HCF of 6314,5740 is 574.
Lets's calculate GCF of 6314,5740
| 2 | 6314, 5740 |
| 7 | 3157, 2870 |
| 41 | 451, 410 |
| 11, 10 |
∴ So the GCF of the given numbers is 2 x 7 x 41 = 574
Greatest Common Factor of 6314,5740 By Matching Biggest Common Factor Method
Now, list down the factors of 6314
:1,2,7,11,14,22,41,77,82,154,287,451,574,902,3157,6314
Now, list down the factors of 5740
:1,2,4,5,7,10,14,20,28,35,41,70,82,140,164,205,287,410,574,820,1148,1435,2870,5740
Greatest Common Factor
We found the factors 6314,5740 . The biggest common factor number is the GCF number.
So the greatest common factor 6314,5740 is 574.
Lets's calculate LCM of 974,5639
Given numbers has no common factors except 1. So, there LCM is their product i.e 5492386
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 574/5492386
Therefore, the GCF of Fractions 6314/974,5740/5639 is 574/5492386
Least Common Multiple of 974,5639 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 974,5639 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(974,5639) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(974,5639) x common factors =1 x 1 = 1
LCM(974,5639) = ( 974 × 5639 ) / 1
LCM(974,5639) = 5492386 / 1
LCM(974,5639) = 5492386
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FAQs on GCF of Fractions of 6314/974, 5740/5639
1. What is the HCF of 6314,5740?
The HCF of 6314,5740 is 574
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 6314/974, 5740/5639?
Answer: GCF of Numerators as per given numbers 6314/974, 5740/5639 is
GCF of Numerators i.e. for 6314,5740 is 574
LCM of denominators i.e. for 974,5639 is 5492386.
Thus, GCF of Fractions is 574/5492386.Finally, GCF of Fractions for 6314/974, 5740/5639 is 574/5492386.