GCF of 4140/132, 4022/2564
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4140/132, 4022/2564 i.e 2/84612 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4140/132, 4022/2564.
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 4140/132,4022/2564?
Given fractions are 4140/132,4022/2564
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 4140/132,4022/2564, numerators are 4140,4022
Denominators are 132,2564
The GCF of 4140,4022 is 2 .
LCM of 132,2564 is 84612.
The greatest common factor of 4140/132,4022/2564 = [GCF of 4140,4022]/[LCM of 132,2564]= 2/84612
Therefore, the GCF of 4140/132,4022/2564 is 2/84612.
To find the highest common factor of 4140,4022, we have to find the factors of both numbers and list the highest common factor.
The factors of 4140 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 23, 30, 36, 45, 46, 60, 69, 90, 92, 115, 138, 180, 207, 230, 276, 345, 414, 460, 690, 828, 1035, 1380, 2070, 4140
The factors of 4022 are 1, 2, 2011, 4022
The HCF of 4140,4022 is 2.
Lets's calculate GCF of 4140,4022
| 2 | 4140, 4022 |
| 2070, 2011 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4140,4022 By Matching Biggest Common Factor Method
Now, list down the factors of 4140
:1,2,3,4,5,6,9,10,12,15,18,20,23,30,36,45,46,60,69,90,92,115,138,180,207,230,276,345,414,460,690,828,1035,1380,2070,4140
Now, list down the factors of 4022
:1,2,2011,4022
Greatest Common Factor
We found the factors 4140,4022 . The biggest common factor number is the GCF number.
So the greatest common factor 4140,4022 is 2.
Lets's calculate LCM of 132,2564
| 2 | 132, 2564 |
| 2 | 66, 1282 |
| 33, 641 |
∴ So the LCM of the given numbers is 2 x 2 x 33 x 641 = 84612
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/84612
Therefore, the GCF of Fractions 4140/132,4022/2564 is 2/84612
Least Common Multiple of 132,2564 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 132,2564 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(132,2564) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(132,2564) x common factors =4 x 1 = 4
LCM(132,2564) = ( 132 × 2564 ) / 4
LCM(132,2564) = 338448 / 4
LCM(132,2564) = 84612
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FAQs on GCF of Fractions of 4140/132, 4022/2564
1. What is the HCF of 4140,4022?
The HCF of 4140,4022 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 4140/132, 4022/2564?
Answer: GCF of Numerators as per given numbers 4140/132, 4022/2564 is
GCF of Numerators i.e. for 4140,4022 is 2
LCM of denominators i.e. for 132,2564 is 84612.
Thus, GCF of Fractions is 2/84612.Finally, GCF of Fractions for 4140/132, 4022/2564 is 2/84612.