GCF of 970/705, 514/108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 970/705, 514/108 i.e 2/25380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 970/705, 514/108.
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 970/705,514/108?
Given fractions are 970/705,514/108
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 970/705,514/108, numerators are 970,514
Denominators are 705,108
The GCF of 970,514 is 2 .
LCM of 705,108 is 25380.
The greatest common factor of 970/705,514/108 = [GCF of 970,514]/[LCM of 705,108]= 2/25380
Therefore, the GCF of 970/705,514/108 is 2/25380.
To find the highest common factor of 970,514, we have to find the factors of both numbers and list the highest common factor.
The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970
The factors of 514 are 1, 2, 257, 514
The HCF of 970,514 is 2.
Lets's calculate GCF of 970,514
| 2 | 970, 514 |
| 485, 257 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 970,514 By Matching Biggest Common Factor Method
Now, list down the factors of 970
:1,2,5,10,97,194,485,970
Now, list down the factors of 514
:1,2,257,514
Greatest Common Factor
We found the factors 970,514 . The biggest common factor number is the GCF number.
So the greatest common factor 970,514 is 2.
Lets's calculate LCM of 705,108
| 3 | 705, 108 |
| 235, 36 |
∴ So the LCM of the given numbers is 3 x 235 x 36 = 25380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25380
Therefore, the GCF of Fractions 970/705,514/108 is 2/25380
Least Common Multiple of 705,108 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 705,108 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(705,108) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(705,108) x common factors =3 x 1 = 3
LCM(705,108) = ( 705 × 108 ) / 3
LCM(705,108) = 76140 / 3
LCM(705,108) = 25380
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FAQs on GCF of Fractions of 970/705, 514/108
1. What is the HCF of 970,514?
The HCF of 970,514 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 970/705, 514/108?
Answer: GCF of Numerators as per given numbers 970/705, 514/108 is
GCF of Numerators i.e. for 970,514 is 2
LCM of denominators i.e. for 705,108 is 25380.
Thus, GCF of Fractions is 2/25380.Finally, GCF of Fractions for 970/705, 514/108 is 2/25380.