GCF of 34/97, 780/56, 266/136
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/97, 780/56, 266/136 i.e 2/92344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/97, 780/56, 266/136.
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 34/97,780/56,266/136?
Given fractions are 34/97,780/56,266/136
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 34/97,780/56,266/136, numerators are 34,780,266
Denominators are 97,56,136
The GCF of 34,780,266 is 2 .
LCM of 97,56,136 is 92344.
The greatest common factor of 34/97,780/56,266/136 = [GCF of 34,780,266]/[LCM of 97,56,136]= 2/92344
Therefore, the GCF of 34/97,780/56,266/136 is 2/92344.
To find the highest common factor of 34,780,266, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266
The HCF of 34,780,266 is 2.
Lets's calculate GCF of 34,780,266
| 2 | 34, 780, 266 |
| 17, 390, 133 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 34,780,266 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Now, list down the factors of 266
:1,2,7,14,19,38,133,266
Greatest Common Factor
We found the factors 34,780,266 . The biggest common factor number is the GCF number.
So the greatest common factor 34,780,266 is 2.
Lets's calculate LCM of 97,56,136
| 2 | 97, 56, 136 |
| 2 | 97, 28, 68 |
| 2 | 97, 14, 34 |
| 97, 7, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 97 x 7 x 17 = 92344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/92344
Therefore, the GCF of Fractions 34/97,780/56,266/136 is 2/92344
Least Common Multiple of 97,56,136 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 97,56,136 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(97,56,136) = 1
common factors(in case of two or more numbers have common factors) = 8
GCF(97,56,136) x common factors =1 x 8 = 8
LCM(97,56,136) = ( 97 × 56 × 136 ) / 8
LCM(97,56,136) = 738752 / 8
LCM(97,56,136) = 92344
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FAQs on GCF of Fractions of 34/97, 780/56, 266/136
1. What is the HCF of 34,780,266?
The HCF of 34,780,266 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 34/97, 780/56, 266/136?
Answer: GCF of Numerators as per given numbers 34/97, 780/56, 266/136 is
GCF of Numerators i.e. for 34,780,266 is 2
LCM of denominators i.e. for 97,56,136 is 92344.
Thus, GCF of Fractions is 2/92344.Finally, GCF of Fractions for 34/97, 780/56, 266/136 is 2/92344.