GCF of 634/51, 114/509
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 634/51, 114/509 i.e 2/25959 easily. The following is the detailed procedure to determine the greatest common factor of fractions 634/51, 114/509.
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 634/51,114/509?
Given fractions are 634/51,114/509
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 634/51,114/509, numerators are 634,114
Denominators are 51,509
The GCF of 634,114 is 2 .
LCM of 51,509 is 25959.
The greatest common factor of 634/51,114/509 = [GCF of 634,114]/[LCM of 51,509]= 2/25959
Therefore, the GCF of 634/51,114/509 is 2/25959.
To find the highest common factor of 634,114, we have to find the factors of both numbers and list the highest common factor.
The factors of 634 are 1, 2, 317, 634
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 634,114 is 2.
Lets's calculate GCF of 634,114
| 2 | 634, 114 |
| 317, 57 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 634,114 By Matching Biggest Common Factor Method
Now, list down the factors of 634
:1,2,317,634
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 634,114 . The biggest common factor number is the GCF number.
So the greatest common factor 634,114 is 2.
Lets's calculate LCM of 51,509
Given numbers has no common factors except 1. So, there LCM is their product i.e 25959
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25959
Therefore, the GCF of Fractions 634/51,114/509 is 2/25959
Least Common Multiple of 51,509 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 51,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,509) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,509) x common factors =1 x 1 = 1
LCM(51,509) = ( 51 × 509 ) / 1
LCM(51,509) = 25959 / 1
LCM(51,509) = 25959
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FAQs on GCF of Fractions of 634/51, 114/509
1. What is the HCF of 634,114?
The HCF of 634,114 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 634/51, 114/509?
Answer: GCF of Numerators as per given numbers 634/51, 114/509 is
GCF of Numerators i.e. for 634,114 is 2
LCM of denominators i.e. for 51,509 is 25959.
Thus, GCF of Fractions is 2/25959.Finally, GCF of Fractions for 634/51, 114/509 is 2/25959.