GCF of 7605/71, 2262/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7605/71, 2262/419 i.e 39/29749 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7605/71, 2262/419.
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 7605/71,2262/419?
Given fractions are 7605/71,2262/419
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 7605/71,2262/419, numerators are 7605,2262
Denominators are 71,419
The GCF of 7605,2262 is 39 .
LCM of 71,419 is 29749.
The greatest common factor of 7605/71,2262/419 = [GCF of 7605,2262]/[LCM of 71,419]= 39/29749
Therefore, the GCF of 7605/71,2262/419 is 39/29749.
To find the highest common factor of 7605,2262, we have to find the factors of both numbers and list the highest common factor.
The factors of 7605 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 169, 195, 507, 585, 845, 1521, 2535, 7605
The factors of 2262 are 1, 2, 3, 6, 13, 26, 29, 39, 58, 78, 87, 174, 377, 754, 1131, 2262
The HCF of 7605,2262 is 39.
Lets's calculate GCF of 7605,2262
| 3 | 7605, 2262 |
| 13 | 2535, 754 |
| 195, 58 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Greatest Common Factor of 7605,2262 By Matching Biggest Common Factor Method
Now, list down the factors of 7605
:1,3,5,9,13,15,39,45,65,117,169,195,507,585,845,1521,2535,7605
Now, list down the factors of 2262
:1,2,3,6,13,26,29,39,58,78,87,174,377,754,1131,2262
Greatest Common Factor
We found the factors 7605,2262 . The biggest common factor number is the GCF number.
So the greatest common factor 7605,2262 is 39.
Lets's calculate LCM of 71,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 29749
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/29749
Therefore, the GCF of Fractions 7605/71,2262/419 is 39/29749
Least Common Multiple of 71,419 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 71,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,419) x common factors =1 x 1 = 1
LCM(71,419) = ( 71 × 419 ) / 1
LCM(71,419) = 29749 / 1
LCM(71,419) = 29749
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FAQs on GCF of Fractions of 7605/71, 2262/419
1. What is the HCF of 7605,2262?
The HCF of 7605,2262 is 39
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 7605/71, 2262/419?
Answer: GCF of Numerators as per given numbers 7605/71, 2262/419 is
GCF of Numerators i.e. for 7605,2262 is 39
LCM of denominators i.e. for 71,419 is 29749.
Thus, GCF of Fractions is 39/29749.Finally, GCF of Fractions for 7605/71, 2262/419 is 39/29749.