GCF of 102/11, 420/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/11, 420/378 i.e 6/4158 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/11, 420/378.
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 102/11,420/378?
Given fractions are 102/11,420/378
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 102/11,420/378, numerators are 102,420
Denominators are 11,378
The GCF of 102,420 is 6 .
LCM of 11,378 is 4158.
The greatest common factor of 102/11,420/378 = [GCF of 102,420]/[LCM of 11,378]= 6/4158
Therefore, the GCF of 102/11,420/378 is 6/4158.
To find the highest common factor of 102,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 102,420 is 6.
Lets's calculate GCF of 102,420
| 2 | 102, 420 |
| 3 | 51, 210 |
| 17, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 102,420 By Matching Biggest Common Factor Method
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 102,420 . The biggest common factor number is the GCF number.
So the greatest common factor 102,420 is 6.
Lets's calculate LCM of 11,378
Given numbers has no common factors except 1. So, there LCM is their product i.e 4158
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4158
Therefore, the GCF of Fractions 102/11,420/378 is 6/4158
Least Common Multiple of 11,378 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 11,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(11,378) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(11,378) x common factors =1 x 1 = 1
LCM(11,378) = ( 11 × 378 ) / 1
LCM(11,378) = 4158 / 1
LCM(11,378) = 4158
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FAQs on GCF of Fractions of 102/11, 420/378
1. What is the HCF of 102,420?
The HCF of 102,420 is 6
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 102/11, 420/378?
Answer: GCF of Numerators as per given numbers 102/11, 420/378 is
GCF of Numerators i.e. for 102,420 is 6
LCM of denominators i.e. for 11,378 is 4158.
Thus, GCF of Fractions is 6/4158.Finally, GCF of Fractions for 102/11, 420/378 is 6/4158.