GCF of 6534/306, 8228/7752
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6534/306, 8228/7752 i.e 242/23256 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6534/306, 8228/7752.
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 6534/306,8228/7752?
Given fractions are 6534/306,8228/7752
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 6534/306,8228/7752, numerators are 6534,8228
Denominators are 306,7752
The GCF of 6534,8228 is 242 .
LCM of 306,7752 is 23256.
The greatest common factor of 6534/306,8228/7752 = [GCF of 6534,8228]/[LCM of 306,7752]= 242/23256
Therefore, the GCF of 6534/306,8228/7752 is 242/23256.
To find the highest common factor of 6534,8228, we have to find the factors of both numbers and list the highest common factor.
The factors of 6534 are 1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 121, 198, 242, 297, 363, 594, 726, 1089, 2178, 3267, 6534
The factors of 8228 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 121, 187, 242, 374, 484, 748, 2057, 4114, 8228
The HCF of 6534,8228 is 242.
Lets's calculate GCF of 6534,8228
| 2 | 6534, 8228 |
| 11 | 3267, 4114 |
| 11 | 297, 374 |
| 27, 34 |
∴ So the GCF of the given numbers is 2 x 11 x 11 = 242
Greatest Common Factor of 6534,8228 By Matching Biggest Common Factor Method
Now, list down the factors of 6534
:1,2,3,6,9,11,18,22,27,33,54,66,99,121,198,242,297,363,594,726,1089,2178,3267,6534
Now, list down the factors of 8228
:1,2,4,11,17,22,34,44,68,121,187,242,374,484,748,2057,4114,8228
Greatest Common Factor
We found the factors 6534,8228 . The biggest common factor number is the GCF number.
So the greatest common factor 6534,8228 is 242.
Lets's calculate LCM of 306,7752
| 2 | 306, 7752 |
| 3 | 153, 3876 |
| 17 | 51, 1292 |
| 3, 76 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 3 x 76 = 23256
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 242/23256
Therefore, the GCF of Fractions 6534/306,8228/7752 is 242/23256
Least Common Multiple of 306,7752 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 306,7752 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(306,7752) = 102
common factors(in case of two or more numbers have common factors) = 1
GCF(306,7752) x common factors =102 x 1 = 102
LCM(306,7752) = ( 306 × 7752 ) / 102
LCM(306,7752) = 2372112 / 102
LCM(306,7752) = 23256
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FAQs on GCF of Fractions of 6534/306, 8228/7752
1. What is the HCF of 6534,8228?
The HCF of 6534,8228 is 242
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 6534/306, 8228/7752?
Answer: GCF of Numerators as per given numbers 6534/306, 8228/7752 is
GCF of Numerators i.e. for 6534,8228 is 242
LCM of denominators i.e. for 306,7752 is 23256.
Thus, GCF of Fractions is 242/23256.Finally, GCF of Fractions for 6534/306, 8228/7752 is 242/23256.