GCF of 228/676, 3078/676
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 228/676, 3078/676 i.e 114/676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 228/676, 3078/676.
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 228/676,3078/676?
Given fractions are 228/676,3078/676
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 228/676,3078/676, numerators are 228,3078
Denominators are 676,676
The GCF of 228,3078 is 114 .
LCM of 676,676 is 676.
The greatest common factor of 228/676,3078/676 = [GCF of 228,3078]/[LCM of 676,676]= 114/676
Therefore, the GCF of 228/676,3078/676 is 114/676.
To find the highest common factor of 228,3078, we have to find the factors of both numbers and list the highest common factor.
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The factors of 3078 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078
The HCF of 228,3078 is 114.
Lets's calculate GCF of 228,3078
| 2 | 228, 3078 |
| 3 | 114, 1539 |
| 19 | 38, 513 |
| 2, 27 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Greatest Common Factor of 228,3078 By Matching Biggest Common Factor Method
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Now, list down the factors of 3078
:1,2,3,6,9,18,19,27,38,54,57,81,114,162,171,342,513,1026,1539,3078
Greatest Common Factor
We found the factors 228,3078 . The biggest common factor number is the GCF number.
So the greatest common factor 228,3078 is 114.
Lets's calculate LCM of 676,676
| 2 | 676, 676 |
| 2 | 338, 338 |
| 13 | 169, 169 |
| 13 | 13, 13 |
| 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 13 x 1 x 1 = 676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/676
Therefore, the GCF of Fractions 228/676,3078/676 is 114/676
Least Common Multiple of 676,676 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 676,676 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(676,676) = 676
common factors(in case of two or more numbers have common factors) = 1
GCF(676,676) x common factors =676 x 1 = 676
LCM(676,676) = ( 676 × 676 ) / 676
LCM(676,676) = 456976 / 676
LCM(676,676) = 676
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FAQs on GCF of Fractions of 228/676, 3078/676
1. What is the HCF of 228,3078?
The HCF of 228,3078 is 114
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 228/676, 3078/676?
Answer: GCF of Numerators as per given numbers 228/676, 3078/676 is
GCF of Numerators i.e. for 228,3078 is 114
LCM of denominators i.e. for 676,676 is 676.
Thus, GCF of Fractions is 114/676.Finally, GCF of Fractions for 228/676, 3078/676 is 114/676.