GCF of 3128/469, 2070/418
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3128/469, 2070/418 i.e 46/196042 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3128/469, 2070/418.
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 3128/469,2070/418?
Given fractions are 3128/469,2070/418
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 3128/469,2070/418, numerators are 3128,2070
Denominators are 469,418
The GCF of 3128,2070 is 46 .
LCM of 469,418 is 196042.
The greatest common factor of 3128/469,2070/418 = [GCF of 3128,2070]/[LCM of 469,418]= 46/196042
Therefore, the GCF of 3128/469,2070/418 is 46/196042.
To find the highest common factor of 3128,2070, we have to find the factors of both numbers and list the highest common factor.
The factors of 3128 are 1, 2, 4, 8, 17, 23, 34, 46, 68, 92, 136, 184, 391, 782, 1564, 3128
The factors of 2070 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 23, 30, 45, 46, 69, 90, 115, 138, 207, 230, 345, 414, 690, 1035, 2070
The HCF of 3128,2070 is 46.
Lets's calculate GCF of 3128,2070
| 2 | 3128, 2070 |
| 23 | 1564, 1035 |
| 68, 45 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 3128,2070 By Matching Biggest Common Factor Method
Now, list down the factors of 3128
:1,2,4,8,17,23,34,46,68,92,136,184,391,782,1564,3128
Now, list down the factors of 2070
:1,2,3,5,6,9,10,15,18,23,30,45,46,69,90,115,138,207,230,345,414,690,1035,2070
Greatest Common Factor
We found the factors 3128,2070 . The biggest common factor number is the GCF number.
So the greatest common factor 3128,2070 is 46.
Lets's calculate LCM of 469,418
Given numbers has no common factors except 1. So, there LCM is their product i.e 196042
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/196042
Therefore, the GCF of Fractions 3128/469,2070/418 is 46/196042
Least Common Multiple of 469,418 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 469,418 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(469,418) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(469,418) x common factors =1 x 1 = 1
LCM(469,418) = ( 469 × 418 ) / 1
LCM(469,418) = 196042 / 1
LCM(469,418) = 196042
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FAQs on GCF of Fractions of 3128/469, 2070/418
1. What is the HCF of 3128,2070?
The HCF of 3128,2070 is 46
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 3128/469, 2070/418?
Answer: GCF of Numerators as per given numbers 3128/469, 2070/418 is
GCF of Numerators i.e. for 3128,2070 is 46
LCM of denominators i.e. for 469,418 is 196042.
Thus, GCF of Fractions is 46/196042.Finally, GCF of Fractions for 3128/469, 2070/418 is 46/196042.