GCF of 4158/254, 3420/3410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4158/254, 3420/3410 i.e 18/433070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4158/254, 3420/3410.
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 4158/254,3420/3410?
Given fractions are 4158/254,3420/3410
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 4158/254,3420/3410, numerators are 4158,3420
Denominators are 254,3410
The GCF of 4158,3420 is 18 .
LCM of 254,3410 is 433070.
The greatest common factor of 4158/254,3420/3410 = [GCF of 4158,3420]/[LCM of 254,3410]= 18/433070
Therefore, the GCF of 4158/254,3420/3410 is 18/433070.
To find the highest common factor of 4158,3420, we have to find the factors of both numbers and list the highest common factor.
The factors of 4158 are 1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 27, 33, 42, 54, 63, 66, 77, 99, 126, 154, 189, 198, 231, 297, 378, 462, 594, 693, 1386, 2079, 4158
The factors of 3420 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710, 3420
The HCF of 4158,3420 is 18.
Lets's calculate GCF of 4158,3420
| 2 | 4158, 3420 |
| 3 | 2079, 1710 |
| 3 | 693, 570 |
| 231, 190 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 4158,3420 By Matching Biggest Common Factor Method
Now, list down the factors of 4158
:1,2,3,6,7,9,11,14,18,21,22,27,33,42,54,63,66,77,99,126,154,189,198,231,297,378,462,594,693,1386,2079,4158
Now, list down the factors of 3420
:1,2,3,4,5,6,9,10,12,15,18,19,20,30,36,38,45,57,60,76,90,95,114,171,180,190,228,285,342,380,570,684,855,1140,1710,3420
Greatest Common Factor
We found the factors 4158,3420 . The biggest common factor number is the GCF number.
So the greatest common factor 4158,3420 is 18.
Lets's calculate LCM of 254,3410
| 2 | 254, 3410 |
| 127, 1705 |
∴ So the LCM of the given numbers is 2 x 127 x 1705 = 433070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/433070
Therefore, the GCF of Fractions 4158/254,3420/3410 is 18/433070
Least Common Multiple of 254,3410 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 254,3410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(254,3410) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(254,3410) x common factors =2 x 1 = 2
LCM(254,3410) = ( 254 × 3410 ) / 2
LCM(254,3410) = 866140 / 2
LCM(254,3410) = 433070
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FAQs on GCF of Fractions of 4158/254, 3420/3410
1. What is the HCF of 4158,3420?
The HCF of 4158,3420 is 18
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 4158/254, 3420/3410?
Answer: GCF of Numerators as per given numbers 4158/254, 3420/3410 is
GCF of Numerators i.e. for 4158,3420 is 18
LCM of denominators i.e. for 254,3410 is 433070.
Thus, GCF of Fractions is 18/433070.Finally, GCF of Fractions for 4158/254, 3420/3410 is 18/433070.