GCF of 7725/164, 7074/710
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7725/164, 7074/710 i.e 3/58220 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7725/164, 7074/710.
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 7725/164,7074/710?
Given fractions are 7725/164,7074/710
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 7725/164,7074/710, numerators are 7725,7074
Denominators are 164,710
The GCF of 7725,7074 is 3 .
LCM of 164,710 is 58220.
The greatest common factor of 7725/164,7074/710 = [GCF of 7725,7074]/[LCM of 164,710]= 3/58220
Therefore, the GCF of 7725/164,7074/710 is 3/58220.
To find the highest common factor of 7725,7074, we have to find the factors of both numbers and list the highest common factor.
The factors of 7725 are 1, 3, 5, 15, 25, 75, 103, 309, 515, 1545, 2575, 7725
The factors of 7074 are 1, 2, 3, 6, 9, 18, 27, 54, 131, 262, 393, 786, 1179, 2358, 3537, 7074
The HCF of 7725,7074 is 3.
Lets's calculate GCF of 7725,7074
| 3 | 7725, 7074 |
| 2575, 2358 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7725,7074 By Matching Biggest Common Factor Method
Now, list down the factors of 7725
:1,3,5,15,25,75,103,309,515,1545,2575,7725
Now, list down the factors of 7074
:1,2,3,6,9,18,27,54,131,262,393,786,1179,2358,3537,7074
Greatest Common Factor
We found the factors 7725,7074 . The biggest common factor number is the GCF number.
So the greatest common factor 7725,7074 is 3.
Lets's calculate LCM of 164,710
| 2 | 164, 710 |
| 82, 355 |
∴ So the LCM of the given numbers is 2 x 82 x 355 = 58220
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/58220
Therefore, the GCF of Fractions 7725/164,7074/710 is 3/58220
Least Common Multiple of 164,710 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 164,710 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,710) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,710) x common factors =2 x 1 = 2
LCM(164,710) = ( 164 × 710 ) / 2
LCM(164,710) = 116440 / 2
LCM(164,710) = 58220
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FAQs on GCF of Fractions of 7725/164, 7074/710
1. What is the HCF of 7725,7074?
The HCF of 7725,7074 is 3
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 7725/164, 7074/710?
Answer: GCF of Numerators as per given numbers 7725/164, 7074/710 is
GCF of Numerators i.e. for 7725,7074 is 3
LCM of denominators i.e. for 164,710 is 58220.
Thus, GCF of Fractions is 3/58220.Finally, GCF of Fractions for 7725/164, 7074/710 is 3/58220.