GCF of 366/28, 420/1412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 366/28, 420/1412 i.e 6/9884 easily. The following is the detailed procedure to determine the greatest common factor of fractions 366/28, 420/1412.
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 366/28,420/1412?
Given fractions are 366/28,420/1412
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 366/28,420/1412, numerators are 366,420
Denominators are 28,1412
The GCF of 366,420 is 6 .
LCM of 28,1412 is 9884.
The greatest common factor of 366/28,420/1412 = [GCF of 366,420]/[LCM of 28,1412]= 6/9884
Therefore, the GCF of 366/28,420/1412 is 6/9884.
To find the highest common factor of 366,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 366 are 1, 2, 3, 6, 61, 122, 183, 366
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 366,420 is 6.
Lets's calculate GCF of 366,420
| 2 | 366, 420 |
| 3 | 183, 210 |
| 61, 70 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 366,420 By Matching Biggest Common Factor Method
Now, list down the factors of 366
:1,2,3,6,61,122,183,366
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 366,420 . The biggest common factor number is the GCF number.
So the greatest common factor 366,420 is 6.
Lets's calculate LCM of 28,1412
| 2 | 28, 1412 |
| 2 | 14, 706 |
| 7, 353 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 353 = 9884
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/9884
Therefore, the GCF of Fractions 366/28,420/1412 is 6/9884
Least Common Multiple of 28,1412 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 28,1412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,1412) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(28,1412) x common factors =4 x 1 = 4
LCM(28,1412) = ( 28 × 1412 ) / 4
LCM(28,1412) = 39536 / 4
LCM(28,1412) = 9884
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FAQs on GCF of Fractions of 366/28, 420/1412
1. What is the HCF of 366,420?
The HCF of 366,420 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 366/28, 420/1412?
Answer: GCF of Numerators as per given numbers 366/28, 420/1412 is
GCF of Numerators i.e. for 366,420 is 6
LCM of denominators i.e. for 28,1412 is 9884.
Thus, GCF of Fractions is 6/9884.Finally, GCF of Fractions for 366/28, 420/1412 is 6/9884.