GCF of 3654/522, 5972/164
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3654/522, 5972/164 i.e 2/42804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3654/522, 5972/164.
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 3654/522,5972/164?
Given fractions are 3654/522,5972/164
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 3654/522,5972/164, numerators are 3654,5972
Denominators are 522,164
The GCF of 3654,5972 is 2 .
LCM of 522,164 is 42804.
The greatest common factor of 3654/522,5972/164 = [GCF of 3654,5972]/[LCM of 522,164]= 2/42804
Therefore, the GCF of 3654/522,5972/164 is 2/42804.
To find the highest common factor of 3654,5972, we have to find the factors of both numbers and list the highest common factor.
The factors of 3654 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 29, 42, 58, 63, 87, 126, 174, 203, 261, 406, 522, 609, 1218, 1827, 3654
The factors of 5972 are 1, 2, 4, 1493, 2986, 5972
The HCF of 3654,5972 is 2.
Lets's calculate GCF of 3654,5972
| 2 | 3654, 5972 |
| 1827, 2986 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3654,5972 By Matching Biggest Common Factor Method
Now, list down the factors of 3654
:1,2,3,6,7,9,14,18,21,29,42,58,63,87,126,174,203,261,406,522,609,1218,1827,3654
Now, list down the factors of 5972
:1,2,4,1493,2986,5972
Greatest Common Factor
We found the factors 3654,5972 . The biggest common factor number is the GCF number.
So the greatest common factor 3654,5972 is 2.
Lets's calculate LCM of 522,164
| 2 | 522, 164 |
| 261, 82 |
∴ So the LCM of the given numbers is 2 x 261 x 82 = 42804
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/42804
Therefore, the GCF of Fractions 3654/522,5972/164 is 2/42804
Least Common Multiple of 522,164 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 522,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(522,164) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(522,164) x common factors =2 x 1 = 2
LCM(522,164) = ( 522 × 164 ) / 2
LCM(522,164) = 85608 / 2
LCM(522,164) = 42804
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FAQs on GCF of Fractions of 3654/522, 5972/164
1. What is the HCF of 3654,5972?
The HCF of 3654,5972 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 3654/522, 5972/164?
Answer: GCF of Numerators as per given numbers 3654/522, 5972/164 is
GCF of Numerators i.e. for 3654,5972 is 2
LCM of denominators i.e. for 522,164 is 42804.
Thus, GCF of Fractions is 2/42804.Finally, GCF of Fractions for 3654/522, 5972/164 is 2/42804.