GCF of 546/478, 234/748
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 546/478, 234/748 i.e 78/178772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 546/478, 234/748.
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 546/478,234/748?
Given fractions are 546/478,234/748
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 546/478,234/748, numerators are 546,234
Denominators are 478,748
The GCF of 546,234 is 78 .
LCM of 478,748 is 178772.
The greatest common factor of 546/478,234/748 = [GCF of 546,234]/[LCM of 478,748]= 78/178772
Therefore, the GCF of 546/478,234/748 is 78/178772.
To find the highest common factor of 546,234, we have to find the factors of both numbers and list the highest common factor.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234
The HCF of 546,234 is 78.
Lets's calculate GCF of 546,234
| 2 | 546, 234 |
| 3 | 273, 117 |
| 13 | 91, 39 |
| 7, 3 |
∴ So the GCF of the given numbers is 2 x 3 x 13 = 78
Greatest Common Factor of 546,234 By Matching Biggest Common Factor Method
Now, list down the factors of 546
:1,2,3,6,7,13,14,21,26,39,42,78,91,182,273,546
Now, list down the factors of 234
:1,2,3,6,9,13,18,26,39,78,117,234
Greatest Common Factor
We found the factors 546,234 . The biggest common factor number is the GCF number.
So the greatest common factor 546,234 is 78.
Lets's calculate LCM of 478,748
| 2 | 478, 748 |
| 239, 374 |
∴ So the LCM of the given numbers is 2 x 239 x 374 = 178772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 78/178772
Therefore, the GCF of Fractions 546/478,234/748 is 78/178772
Least Common Multiple of 478,748 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 478,748 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(478,748) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(478,748) x common factors =2 x 1 = 2
LCM(478,748) = ( 478 × 748 ) / 2
LCM(478,748) = 357544 / 2
LCM(478,748) = 178772
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FAQs on GCF of Fractions of 546/478, 234/748
1. What is the HCF of 546,234?
The HCF of 546,234 is 78
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 546/478, 234/748?
Answer: GCF of Numerators as per given numbers 546/478, 234/748 is
GCF of Numerators i.e. for 546,234 is 78
LCM of denominators i.e. for 478,748 is 178772.
Thus, GCF of Fractions is 78/178772.Finally, GCF of Fractions for 546/478, 234/748 is 78/178772.