GCF of 679/16, 970/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 679/16, 970/214 i.e 97/1712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 679/16, 970/214.
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 679/16,970/214?
Given fractions are 679/16,970/214
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 679/16,970/214, numerators are 679,970
Denominators are 16,214
The GCF of 679,970 is 97 .
LCM of 16,214 is 1712.
The greatest common factor of 679/16,970/214 = [GCF of 679,970]/[LCM of 16,214]= 97/1712
Therefore, the GCF of 679/16,970/214 is 97/1712.
To find the highest common factor of 679,970, we have to find the factors of both numbers and list the highest common factor.
The factors of 679 are 1, 7, 97, 679
The factors of 970 are 1, 2, 5, 10, 97, 194, 485, 970
The HCF of 679,970 is 97.
Lets's calculate GCF of 679,970
| 97 | 679, 970 |
| 7, 10 |
∴ So the GCF of the given numbers is 97 = 97
Greatest Common Factor of 679,970 By Matching Biggest Common Factor Method
Now, list down the factors of 679
:1,7,97,679
Now, list down the factors of 970
:1,2,5,10,97,194,485,970
Greatest Common Factor
We found the factors 679,970 . The biggest common factor number is the GCF number.
So the greatest common factor 679,970 is 97.
Lets's calculate LCM of 16,214
| 2 | 16, 214 |
| 8, 107 |
∴ So the LCM of the given numbers is 2 x 8 x 107 = 1712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 97/1712
Therefore, the GCF of Fractions 679/16,970/214 is 97/1712
Least Common Multiple of 16,214 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 16,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(16,214) x common factors =2 x 1 = 2
LCM(16,214) = ( 16 × 214 ) / 2
LCM(16,214) = 3424 / 2
LCM(16,214) = 1712
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FAQs on GCF of Fractions of 679/16, 970/214
1. What is the HCF of 679,970?
The HCF of 679,970 is 97
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 679/16, 970/214?
Answer: GCF of Numerators as per given numbers 679/16, 970/214 is
GCF of Numerators i.e. for 679,970 is 97
LCM of denominators i.e. for 16,214 is 1712.
Thus, GCF of Fractions is 97/1712.Finally, GCF of Fractions for 679/16, 970/214 is 97/1712.