GCF of 812/22, 420/455
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/22, 420/455 i.e 28/10010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/22, 420/455.
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 812/22,420/455?
Given fractions are 812/22,420/455
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 812/22,420/455, numerators are 812,420
Denominators are 22,455
The GCF of 812,420 is 28 .
LCM of 22,455 is 10010.
The greatest common factor of 812/22,420/455 = [GCF of 812,420]/[LCM of 22,455]= 28/10010
Therefore, the GCF of 812/22,420/455 is 28/10010.
To find the highest common factor of 812,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
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 812,420 is 28.
Lets's calculate GCF of 812,420
| 2 | 812, 420 |
| 2 | 406, 210 |
| 7 | 203, 105 |
| 29, 15 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 812,420 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
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 812,420 . The biggest common factor number is the GCF number.
So the greatest common factor 812,420 is 28.
Lets's calculate LCM of 22,455
Given numbers has no common factors except 1. So, there LCM is their product i.e 10010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/10010
Therefore, the GCF of Fractions 812/22,420/455 is 28/10010
Least Common Multiple of 22,455 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 22,455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(22,455) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(22,455) x common factors =1 x 1 = 1
LCM(22,455) = ( 22 × 455 ) / 1
LCM(22,455) = 10010 / 1
LCM(22,455) = 10010
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FAQs on GCF of Fractions of 812/22, 420/455
1. What is the HCF of 812,420?
The HCF of 812,420 is 28
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 812/22, 420/455?
Answer: GCF of Numerators as per given numbers 812/22, 420/455 is
GCF of Numerators i.e. for 812,420 is 28
LCM of denominators i.e. for 22,455 is 10010.
Thus, GCF of Fractions is 28/10010.Finally, GCF of Fractions for 812/22, 420/455 is 28/10010.