GCF of 5278/67, 3976/828
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5278/67, 3976/828 i.e 14/55476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5278/67, 3976/828.
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 5278/67,3976/828?
Given fractions are 5278/67,3976/828
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 5278/67,3976/828, numerators are 5278,3976
Denominators are 67,828
The GCF of 5278,3976 is 14 .
LCM of 67,828 is 55476.
The greatest common factor of 5278/67,3976/828 = [GCF of 5278,3976]/[LCM of 67,828]= 14/55476
Therefore, the GCF of 5278/67,3976/828 is 14/55476.
To find the highest common factor of 5278,3976, we have to find the factors of both numbers and list the highest common factor.
The factors of 5278 are 1, 2, 7, 13, 14, 26, 29, 58, 91, 182, 203, 377, 406, 754, 2639, 5278
The factors of 3976 are 1, 2, 4, 7, 8, 14, 28, 56, 71, 142, 284, 497, 568, 994, 1988, 3976
The HCF of 5278,3976 is 14.
Lets's calculate GCF of 5278,3976
| 2 | 5278, 3976 |
| 7 | 2639, 1988 |
| 377, 284 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5278,3976 By Matching Biggest Common Factor Method
Now, list down the factors of 5278
:1,2,7,13,14,26,29,58,91,182,203,377,406,754,2639,5278
Now, list down the factors of 3976
:1,2,4,7,8,14,28,56,71,142,284,497,568,994,1988,3976
Greatest Common Factor
We found the factors 5278,3976 . The biggest common factor number is the GCF number.
So the greatest common factor 5278,3976 is 14.
Lets's calculate LCM of 67,828
Given numbers has no common factors except 1. So, there LCM is their product i.e 55476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/55476
Therefore, the GCF of Fractions 5278/67,3976/828 is 14/55476
Least Common Multiple of 67,828 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 67,828 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,828) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,828) x common factors =1 x 1 = 1
LCM(67,828) = ( 67 × 828 ) / 1
LCM(67,828) = 55476 / 1
LCM(67,828) = 55476
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FAQs on GCF of Fractions of 5278/67, 3976/828
1. What is the HCF of 5278,3976?
The HCF of 5278,3976 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 5278/67, 3976/828?
Answer: GCF of Numerators as per given numbers 5278/67, 3976/828 is
GCF of Numerators i.e. for 5278,3976 is 14
LCM of denominators i.e. for 67,828 is 55476.
Thus, GCF of Fractions is 14/55476.Finally, GCF of Fractions for 5278/67, 3976/828 is 14/55476.