GCF of 2154/282, 7076/4272
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2154/282, 7076/4272 i.e 2/200784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2154/282, 7076/4272.
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 2154/282,7076/4272?
Given fractions are 2154/282,7076/4272
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 2154/282,7076/4272, numerators are 2154,7076
Denominators are 282,4272
The GCF of 2154,7076 is 2 .
LCM of 282,4272 is 200784.
The greatest common factor of 2154/282,7076/4272 = [GCF of 2154,7076]/[LCM of 282,4272]= 2/200784
Therefore, the GCF of 2154/282,7076/4272 is 2/200784.
To find the highest common factor of 2154,7076, we have to find the factors of both numbers and list the highest common factor.
The factors of 2154 are 1, 2, 3, 6, 359, 718, 1077, 2154
The factors of 7076 are 1, 2, 4, 29, 58, 61, 116, 122, 244, 1769, 3538, 7076
The HCF of 2154,7076 is 2.
Lets's calculate GCF of 2154,7076
| 2 | 2154, 7076 |
| 1077, 3538 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2154,7076 By Matching Biggest Common Factor Method
Now, list down the factors of 2154
:1,2,3,6,359,718,1077,2154
Now, list down the factors of 7076
:1,2,4,29,58,61,116,122,244,1769,3538,7076
Greatest Common Factor
We found the factors 2154,7076 . The biggest common factor number is the GCF number.
So the greatest common factor 2154,7076 is 2.
Lets's calculate LCM of 282,4272
| 2 | 282, 4272 |
| 3 | 141, 2136 |
| 47, 712 |
∴ So the LCM of the given numbers is 2 x 3 x 47 x 712 = 200784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/200784
Therefore, the GCF of Fractions 2154/282,7076/4272 is 2/200784
Least Common Multiple of 282,4272 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 282,4272 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,4272) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(282,4272) x common factors =6 x 1 = 6
LCM(282,4272) = ( 282 × 4272 ) / 6
LCM(282,4272) = 1204704 / 6
LCM(282,4272) = 200784
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FAQs on GCF of Fractions of 2154/282, 7076/4272
1. What is the HCF of 2154,7076?
The HCF of 2154,7076 is 2
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 2154/282, 7076/4272?
Answer: GCF of Numerators as per given numbers 2154/282, 7076/4272 is
GCF of Numerators i.e. for 2154,7076 is 2
LCM of denominators i.e. for 282,4272 is 200784.
Thus, GCF of Fractions is 2/200784.Finally, GCF of Fractions for 2154/282, 7076/4272 is 2/200784.