GCF of 1122/126, 8874/3408
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1122/126, 8874/3408 i.e 102/71568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1122/126, 8874/3408.
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 1122/126,8874/3408?
Given fractions are 1122/126,8874/3408
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 1122/126,8874/3408, numerators are 1122,8874
Denominators are 126,3408
The GCF of 1122,8874 is 102 .
LCM of 126,3408 is 71568.
The greatest common factor of 1122/126,8874/3408 = [GCF of 1122,8874]/[LCM of 126,3408]= 102/71568
Therefore, the GCF of 1122/126,8874/3408 is 102/71568.
To find the highest common factor of 1122,8874, we have to find the factors of both numbers and list the highest common factor.
The factors of 1122 are 1, 2, 3, 6, 11, 17, 22, 33, 34, 51, 66, 102, 187, 374, 561, 1122
The factors of 8874 are 1, 2, 3, 6, 9, 17, 18, 29, 34, 51, 58, 87, 102, 153, 174, 261, 306, 493, 522, 986, 1479, 2958, 4437, 8874
The HCF of 1122,8874 is 102.
Lets's calculate GCF of 1122,8874
| 2 | 1122, 8874 |
| 3 | 561, 4437 |
| 17 | 187, 1479 |
| 11, 87 |
∴ So the GCF of the given numbers is 2 x 3 x 17 = 102
Greatest Common Factor of 1122,8874 By Matching Biggest Common Factor Method
Now, list down the factors of 1122
:1,2,3,6,11,17,22,33,34,51,66,102,187,374,561,1122
Now, list down the factors of 8874
:1,2,3,6,9,17,18,29,34,51,58,87,102,153,174,261,306,493,522,986,1479,2958,4437,8874
Greatest Common Factor
We found the factors 1122,8874 . The biggest common factor number is the GCF number.
So the greatest common factor 1122,8874 is 102.
Lets's calculate LCM of 126,3408
| 2 | 126, 3408 |
| 3 | 63, 1704 |
| 21, 568 |
∴ So the LCM of the given numbers is 2 x 3 x 21 x 568 = 71568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 102/71568
Therefore, the GCF of Fractions 1122/126,8874/3408 is 102/71568
Least Common Multiple of 126,3408 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 126,3408 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(126,3408) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(126,3408) x common factors =6 x 1 = 6
LCM(126,3408) = ( 126 × 3408 ) / 6
LCM(126,3408) = 429408 / 6
LCM(126,3408) = 71568
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FAQs on GCF of Fractions of 1122/126, 8874/3408
1. What is the HCF of 1122,8874?
The HCF of 1122,8874 is 102
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 1122/126, 8874/3408?
Answer: GCF of Numerators as per given numbers 1122/126, 8874/3408 is
GCF of Numerators i.e. for 1122,8874 is 102
LCM of denominators i.e. for 126,3408 is 71568.
Thus, GCF of Fractions is 102/71568.Finally, GCF of Fractions for 1122/126, 8874/3408 is 102/71568.