GCF of 770/180, 8421/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 770/180, 8421/196 i.e 7/8820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/180, 8421/196.
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 770/180,8421/196?
Given fractions are 770/180,8421/196
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 770/180,8421/196, numerators are 770,8421
Denominators are 180,196
The GCF of 770,8421 is 7 .
LCM of 180,196 is 8820.
The greatest common factor of 770/180,8421/196 = [GCF of 770,8421]/[LCM of 180,196]= 7/8820
Therefore, the GCF of 770/180,8421/196 is 7/8820.
To find the highest common factor of 770,8421, we have to find the factors of both numbers and list the highest common factor.
The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770
The factors of 8421 are 1, 3, 7, 21, 401, 1203, 2807, 8421
The HCF of 770,8421 is 7.
Lets's calculate GCF of 770,8421
| 7 | 770, 8421 |
| 110, 1203 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 770,8421 By Matching Biggest Common Factor Method
Now, list down the factors of 770
:1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770
Now, list down the factors of 8421
:1,3,7,21,401,1203,2807,8421
Greatest Common Factor
We found the factors 770,8421 . The biggest common factor number is the GCF number.
So the greatest common factor 770,8421 is 7.
Lets's calculate LCM of 180,196
| 2 | 180, 196 |
| 2 | 90, 98 |
| 45, 49 |
∴ So the LCM of the given numbers is 2 x 2 x 45 x 49 = 8820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/8820
Therefore, the GCF of Fractions 770/180,8421/196 is 7/8820
Least Common Multiple of 180,196 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 180,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,196) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(180,196) x common factors =4 x 1 = 4
LCM(180,196) = ( 180 × 196 ) / 4
LCM(180,196) = 35280 / 4
LCM(180,196) = 8820
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FAQs on GCF of Fractions of 770/180, 8421/196
1. What is the HCF of 770,8421?
The HCF of 770,8421 is 7
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 770/180, 8421/196?
Answer: GCF of Numerators as per given numbers 770/180, 8421/196 is
GCF of Numerators i.e. for 770,8421 is 7
LCM of denominators i.e. for 180,196 is 8820.
Thus, GCF of Fractions is 7/8820.Finally, GCF of Fractions for 770/180, 8421/196 is 7/8820.