GCF of 986/68, 102/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 986/68, 102/312 i.e 34/5304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 986/68, 102/312.
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 986/68,102/312?
Given fractions are 986/68,102/312
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 986/68,102/312, numerators are 986,102
Denominators are 68,312
The GCF of 986,102 is 34 .
LCM of 68,312 is 5304.
The greatest common factor of 986/68,102/312 = [GCF of 986,102]/[LCM of 68,312]= 34/5304
Therefore, the GCF of 986/68,102/312 is 34/5304.
To find the highest common factor of 986,102, we have to find the factors of both numbers and list the highest common factor.
The factors of 986 are 1, 2, 17, 29, 34, 58, 493, 986
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The HCF of 986,102 is 34.
Lets's calculate GCF of 986,102
| 2 | 986, 102 |
| 17 | 493, 51 |
| 29, 3 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 986,102 By Matching Biggest Common Factor Method
Now, list down the factors of 986
:1,2,17,29,34,58,493,986
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Greatest Common Factor
We found the factors 986,102 . The biggest common factor number is the GCF number.
So the greatest common factor 986,102 is 34.
Lets's calculate LCM of 68,312
| 2 | 68, 312 |
| 2 | 34, 156 |
| 17, 78 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 78 = 5304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/5304
Therefore, the GCF of Fractions 986/68,102/312 is 34/5304
Least Common Multiple of 68,312 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 68,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,312) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(68,312) x common factors =4 x 1 = 4
LCM(68,312) = ( 68 × 312 ) / 4
LCM(68,312) = 21216 / 4
LCM(68,312) = 5304
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FAQs on GCF of Fractions of 986/68, 102/312
1. What is the HCF of 986,102?
The HCF of 986,102 is 34
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 986/68, 102/312?
Answer: GCF of Numerators as per given numbers 986/68, 102/312 is
GCF of Numerators i.e. for 986,102 is 34
LCM of denominators i.e. for 68,312 is 5304.
Thus, GCF of Fractions is 34/5304.Finally, GCF of Fractions for 986/68, 102/312 is 34/5304.