GCF of 3430/465, 2814/8253
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3430/465, 2814/8253 i.e 14/1279215 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3430/465, 2814/8253.
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 3430/465,2814/8253?
Given fractions are 3430/465,2814/8253
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 3430/465,2814/8253, numerators are 3430,2814
Denominators are 465,8253
The GCF of 3430,2814 is 14 .
LCM of 465,8253 is 1279215.
The greatest common factor of 3430/465,2814/8253 = [GCF of 3430,2814]/[LCM of 465,8253]= 14/1279215
Therefore, the GCF of 3430/465,2814/8253 is 14/1279215.
To find the highest common factor of 3430,2814, we have to find the factors of both numbers and list the highest common factor.
The factors of 3430 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 343, 490, 686, 1715, 3430
The factors of 2814 are 1, 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938, 1407, 2814
The HCF of 3430,2814 is 14.
Lets's calculate GCF of 3430,2814
| 2 | 3430, 2814 |
| 7 | 1715, 1407 |
| 245, 201 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 3430,2814 By Matching Biggest Common Factor Method
Now, list down the factors of 3430
:1,2,5,7,10,14,35,49,70,98,245,343,490,686,1715,3430
Now, list down the factors of 2814
:1,2,3,6,7,14,21,42,67,134,201,402,469,938,1407,2814
Greatest Common Factor
We found the factors 3430,2814 . The biggest common factor number is the GCF number.
So the greatest common factor 3430,2814 is 14.
Lets's calculate LCM of 465,8253
| 3 | 465, 8253 |
| 155, 2751 |
∴ So the LCM of the given numbers is 3 x 155 x 2751 = 1279215
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1279215
Therefore, the GCF of Fractions 3430/465,2814/8253 is 14/1279215
Least Common Multiple of 465,8253 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 465,8253 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(465,8253) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(465,8253) x common factors =3 x 1 = 3
LCM(465,8253) = ( 465 × 8253 ) / 3
LCM(465,8253) = 3837645 / 3
LCM(465,8253) = 1279215
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FAQs on GCF of Fractions of 3430/465, 2814/8253
1. What is the HCF of 3430,2814?
The HCF of 3430,2814 is 14
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 3430/465, 2814/8253?
Answer: GCF of Numerators as per given numbers 3430/465, 2814/8253 is
GCF of Numerators i.e. for 3430,2814 is 14
LCM of denominators i.e. for 465,8253 is 1279215.
Thus, GCF of Fractions is 14/1279215.Finally, GCF of Fractions for 3430/465, 2814/8253 is 14/1279215.