GCF of 2214/178, 6502/310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2214/178, 6502/310 i.e 2/27590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2214/178, 6502/310.
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 2214/178,6502/310?
Given fractions are 2214/178,6502/310
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 2214/178,6502/310, numerators are 2214,6502
Denominators are 178,310
The GCF of 2214,6502 is 2 .
LCM of 178,310 is 27590.
The greatest common factor of 2214/178,6502/310 = [GCF of 2214,6502]/[LCM of 178,310]= 2/27590
Therefore, the GCF of 2214/178,6502/310 is 2/27590.
To find the highest common factor of 2214,6502, we have to find the factors of both numbers and list the highest common factor.
The factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214
The factors of 6502 are 1, 2, 3251, 6502
The HCF of 2214,6502 is 2.
Lets's calculate GCF of 2214,6502
| 2 | 2214, 6502 |
| 1107, 3251 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2214,6502 By Matching Biggest Common Factor Method
Now, list down the factors of 2214
:1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214
Now, list down the factors of 6502
:1,2,3251,6502
Greatest Common Factor
We found the factors 2214,6502 . The biggest common factor number is the GCF number.
So the greatest common factor 2214,6502 is 2.
Lets's calculate LCM of 178,310
| 2 | 178, 310 |
| 89, 155 |
∴ So the LCM of the given numbers is 2 x 89 x 155 = 27590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27590
Therefore, the GCF of Fractions 2214/178,6502/310 is 2/27590
Least Common Multiple of 178,310 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 178,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(178,310) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(178,310) x common factors =2 x 1 = 2
LCM(178,310) = ( 178 × 310 ) / 2
LCM(178,310) = 55180 / 2
LCM(178,310) = 27590
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FAQs on GCF of Fractions of 2214/178, 6502/310
1. What is the HCF of 2214,6502?
The HCF of 2214,6502 is 2
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 2214/178, 6502/310?
Answer: GCF of Numerators as per given numbers 2214/178, 6502/310 is
GCF of Numerators i.e. for 2214,6502 is 2
LCM of denominators i.e. for 178,310 is 27590.
Thus, GCF of Fractions is 2/27590.Finally, GCF of Fractions for 2214/178, 6502/310 is 2/27590.