GCF of 798/65, 564/180
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 798/65, 564/180 i.e 6/2340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 798/65, 564/180.
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 798/65,564/180?
Given fractions are 798/65,564/180
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 798/65,564/180, numerators are 798,564
Denominators are 65,180
The GCF of 798,564 is 6 .
LCM of 65,180 is 2340.
The greatest common factor of 798/65,564/180 = [GCF of 798,564]/[LCM of 65,180]= 6/2340
Therefore, the GCF of 798/65,564/180 is 6/2340.
To find the highest common factor of 798,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 798,564 is 6.
Lets's calculate GCF of 798,564
| 2 | 798, 564 |
| 3 | 399, 282 |
| 133, 94 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 798,564 By Matching Biggest Common Factor Method
Now, list down the factors of 798
:1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 798,564 . The biggest common factor number is the GCF number.
So the greatest common factor 798,564 is 6.
Lets's calculate LCM of 65,180
| 5 | 65, 180 |
| 13, 36 |
∴ So the LCM of the given numbers is 5 x 13 x 36 = 2340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/2340
Therefore, the GCF of Fractions 798/65,564/180 is 6/2340
Least Common Multiple of 65,180 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 65,180 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,180) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,180) x common factors =5 x 1 = 5
LCM(65,180) = ( 65 × 180 ) / 5
LCM(65,180) = 11700 / 5
LCM(65,180) = 2340
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FAQs on GCF of Fractions of 798/65, 564/180
1. What is the HCF of 798,564?
The HCF of 798,564 is 6
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 798/65, 564/180?
Answer: GCF of Numerators as per given numbers 798/65, 564/180 is
GCF of Numerators i.e. for 798,564 is 6
LCM of denominators i.e. for 65,180 is 2340.
Thus, GCF of Fractions is 6/2340.Finally, GCF of Fractions for 798/65, 564/180 is 6/2340.