GCF of 518/707, 312/689
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 518/707, 312/689 i.e 2/487123 easily. The following is the detailed procedure to determine the greatest common factor of fractions 518/707, 312/689.
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 518/707,312/689?
Given fractions are 518/707,312/689
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 518/707,312/689, numerators are 518,312
Denominators are 707,689
The GCF of 518,312 is 2 .
LCM of 707,689 is 487123.
The greatest common factor of 518/707,312/689 = [GCF of 518,312]/[LCM of 707,689]= 2/487123
Therefore, the GCF of 518/707,312/689 is 2/487123.
To find the highest common factor of 518,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 518,312 is 2.
Lets's calculate GCF of 518,312
| 2 | 518, 312 |
| 259, 156 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 518,312 By Matching Biggest Common Factor Method
Now, list down the factors of 518
:1,2,7,14,37,74,259,518
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 518,312 . The biggest common factor number is the GCF number.
So the greatest common factor 518,312 is 2.
Lets's calculate LCM of 707,689
Given numbers has no common factors except 1. So, there LCM is their product i.e 487123
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/487123
Therefore, the GCF of Fractions 518/707,312/689 is 2/487123
Least Common Multiple of 707,689 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 707,689 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(707,689) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(707,689) x common factors =1 x 1 = 1
LCM(707,689) = ( 707 × 689 ) / 1
LCM(707,689) = 487123 / 1
LCM(707,689) = 487123
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FAQs on GCF of Fractions of 518/707, 312/689
1. What is the HCF of 518,312?
The HCF of 518,312 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 518/707, 312/689?
Answer: GCF of Numerators as per given numbers 518/707, 312/689 is
GCF of Numerators i.e. for 518,312 is 2
LCM of denominators i.e. for 707,689 is 487123.
Thus, GCF of Fractions is 2/487123.Finally, GCF of Fractions for 518/707, 312/689 is 2/487123.