GCF of 702/509, 221/258
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 702/509, 221/258 i.e 13/131322 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/509, 221/258.
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 702/509,221/258?
Given fractions are 702/509,221/258
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 702/509,221/258, numerators are 702,221
Denominators are 509,258
The GCF of 702,221 is 13 .
LCM of 509,258 is 131322.
The greatest common factor of 702/509,221/258 = [GCF of 702,221]/[LCM of 509,258]= 13/131322
Therefore, the GCF of 702/509,221/258 is 13/131322.
To find the highest common factor of 702,221, we have to find the factors of both numbers and list the highest common factor.
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The factors of 221 are 1, 13, 17, 221
The HCF of 702,221 is 13.
Lets's calculate GCF of 702,221
| 13 | 702, 221 |
| 54, 17 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 702,221 By Matching Biggest Common Factor Method
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Now, list down the factors of 221
:1,13,17,221
Greatest Common Factor
We found the factors 702,221 . The biggest common factor number is the GCF number.
So the greatest common factor 702,221 is 13.
Lets's calculate LCM of 509,258
Given numbers has no common factors except 1. So, there LCM is their product i.e 131322
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/131322
Therefore, the GCF of Fractions 702/509,221/258 is 13/131322
Least Common Multiple of 509,258 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 509,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,258) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,258) x common factors =1 x 1 = 1
LCM(509,258) = ( 509 × 258 ) / 1
LCM(509,258) = 131322 / 1
LCM(509,258) = 131322
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FAQs on GCF of Fractions of 702/509, 221/258
1. What is the HCF of 702,221?
The HCF of 702,221 is 13
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 702/509, 221/258?
Answer: GCF of Numerators as per given numbers 702/509, 221/258 is
GCF of Numerators i.e. for 702,221 is 13
LCM of denominators i.e. for 509,258 is 131322.
Thus, GCF of Fractions is 13/131322.Finally, GCF of Fractions for 702/509, 221/258 is 13/131322.