GCF of 708/269, 778/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 708/269, 778/306 i.e 2/82314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 708/269, 778/306.
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 708/269,778/306?
Given fractions are 708/269,778/306
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 708/269,778/306, numerators are 708,778
Denominators are 269,306
The GCF of 708,778 is 2 .
LCM of 269,306 is 82314.
The greatest common factor of 708/269,778/306 = [GCF of 708,778]/[LCM of 269,306]= 2/82314
Therefore, the GCF of 708/269,778/306 is 2/82314.
To find the highest common factor of 708,778, we have to find the factors of both numbers and list the highest common factor.
The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
The factors of 778 are 1, 2, 389, 778
The HCF of 708,778 is 2.
Lets's calculate GCF of 708,778
| 2 | 708, 778 |
| 354, 389 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 708,778 By Matching Biggest Common Factor Method
Now, list down the factors of 708
:1,2,3,4,6,12,59,118,177,236,354,708
Now, list down the factors of 778
:1,2,389,778
Greatest Common Factor
We found the factors 708,778 . The biggest common factor number is the GCF number.
So the greatest common factor 708,778 is 2.
Lets's calculate LCM of 269,306
Given numbers has no common factors except 1. So, there LCM is their product i.e 82314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/82314
Therefore, the GCF of Fractions 708/269,778/306 is 2/82314
Least Common Multiple of 269,306 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 269,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,306) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,306) x common factors =1 x 1 = 1
LCM(269,306) = ( 269 × 306 ) / 1
LCM(269,306) = 82314 / 1
LCM(269,306) = 82314
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FAQs on GCF of Fractions of 708/269, 778/306
1. What is the HCF of 708,778?
The HCF of 708,778 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 708/269, 778/306?
Answer: GCF of Numerators as per given numbers 708/269, 778/306 is
GCF of Numerators i.e. for 708,778 is 2
LCM of denominators i.e. for 269,306 is 82314.
Thus, GCF of Fractions is 2/82314.Finally, GCF of Fractions for 708/269, 778/306 is 2/82314.