GCF of 126/308, 7138/782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 126/308, 7138/782 i.e 2/120428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 126/308, 7138/782.
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 126/308,7138/782?
Given fractions are 126/308,7138/782
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 126/308,7138/782, numerators are 126,7138
Denominators are 308,782
The GCF of 126,7138 is 2 .
LCM of 308,782 is 120428.
The greatest common factor of 126/308,7138/782 = [GCF of 126,7138]/[LCM of 308,782]= 2/120428
Therefore, the GCF of 126/308,7138/782 is 2/120428.
To find the highest common factor of 126,7138, we have to find the factors of both numbers and list the highest common factor.
The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
The factors of 7138 are 1, 2, 43, 83, 86, 166, 3569, 7138
The HCF of 126,7138 is 2.
Lets's calculate GCF of 126,7138
| 2 | 126, 7138 |
| 63, 3569 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 126,7138 By Matching Biggest Common Factor Method
Now, list down the factors of 126
:1,2,3,6,7,9,14,18,21,42,63,126
Now, list down the factors of 7138
:1,2,43,83,86,166,3569,7138
Greatest Common Factor
We found the factors 126,7138 . The biggest common factor number is the GCF number.
So the greatest common factor 126,7138 is 2.
Lets's calculate LCM of 308,782
| 2 | 308, 782 |
| 154, 391 |
∴ So the LCM of the given numbers is 2 x 154 x 391 = 120428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/120428
Therefore, the GCF of Fractions 126/308,7138/782 is 2/120428
Least Common Multiple of 308,782 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 308,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(308,782) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(308,782) x common factors =2 x 1 = 2
LCM(308,782) = ( 308 × 782 ) / 2
LCM(308,782) = 240856 / 2
LCM(308,782) = 120428
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FAQs on GCF of Fractions of 126/308, 7138/782
1. What is the HCF of 126,7138?
The HCF of 126,7138 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 126/308, 7138/782?
Answer: GCF of Numerators as per given numbers 126/308, 7138/782 is
GCF of Numerators i.e. for 126,7138 is 2
LCM of denominators i.e. for 308,782 is 120428.
Thus, GCF of Fractions is 2/120428.Finally, GCF of Fractions for 126/308, 7138/782 is 2/120428.