GCF of 2732/316, 7138/6860
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2732/316, 7138/6860 i.e 2/541940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2732/316, 7138/6860.
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 2732/316,7138/6860?
Given fractions are 2732/316,7138/6860
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 2732/316,7138/6860, numerators are 2732,7138
Denominators are 316,6860
The GCF of 2732,7138 is 2 .
LCM of 316,6860 is 541940.
The greatest common factor of 2732/316,7138/6860 = [GCF of 2732,7138]/[LCM of 316,6860]= 2/541940
Therefore, the GCF of 2732/316,7138/6860 is 2/541940.
To find the highest common factor of 2732,7138, we have to find the factors of both numbers and list the highest common factor.
The factors of 2732 are 1, 2, 4, 683, 1366, 2732
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The HCF of 2732,7138 is 2.
Lets's calculate GCF of 2732,7138
| 2 | 2732, 7138 |
| 1366, 3569 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2732,7138 By Matching Biggest Common Factor Method
Now, list down the factors of 2732
:1,2,4,683,1366,2732
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Greatest Common Factor
We found the factors 2732,7138 . The biggest common factor number is the GCF number.
So the greatest common factor 2732,7138 is 2.
Lets's calculate LCM of 316,6860
| 2 | 316, 6860 |
| 2 | 158, 3430 |
| 79, 1715 |
∴ So the LCM of the given numbers is 2 x 2 x 79 x 1715 = 541940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/541940
Therefore, the GCF of Fractions 2732/316,7138/6860 is 2/541940
Least Common Multiple of 316,6860 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 316,6860 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(316,6860) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(316,6860) x common factors =4 x 1 = 4
LCM(316,6860) = ( 316 × 6860 ) / 4
LCM(316,6860) = 2167760 / 4
LCM(316,6860) = 541940
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FAQs on GCF of Fractions of 2732/316, 7138/6860
1. What is the HCF of 2732,7138?
The HCF of 2732,7138 is 2
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 2732/316, 7138/6860?
Answer: GCF of Numerators as per given numbers 2732/316, 7138/6860 is
GCF of Numerators i.e. for 2732,7138 is 2
LCM of denominators i.e. for 316,6860 is 541940.
Thus, GCF of Fractions is 2/541940.Finally, GCF of Fractions for 2732/316, 7138/6860 is 2/541940.