GCF of 8175/540, 5434/7672
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8175/540, 5434/7672 i.e 1/1035720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8175/540, 5434/7672.
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 8175/540,5434/7672?
Given fractions are 8175/540,5434/7672
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 8175/540,5434/7672, numerators are 8175,5434
Denominators are 540,7672
The GCF of 8175,5434 is 1 .
LCM of 540,7672 is 1035720.
The greatest common factor of 8175/540,5434/7672 = [GCF of 8175,5434]/[LCM of 540,7672]= 1/1035720
Therefore, the GCF of 8175/540,5434/7672 is 1/1035720.
To find the highest common factor of 8175,5434, we have to find the factors of both numbers and list the highest common factor.
The factors of 8175 are 1, 3, 5, 15, 25, 75, 109, 327, 545, 1635, 2725, 8175
The factors of 5434 are 1, 2, 11, 13, 19, 22, 26, 38, 143, 209, 247, 286, 418, 494, 2717, 5434
The HCF of 8175,5434 is 1.
Lets's calculate GCF of 8175,5434
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8175,5434 By Matching Biggest Common Factor Method
Now, list down the factors of 8175
:1,3,5,15,25,75,109,327,545,1635,2725,8175
Now, list down the factors of 5434
:1,2,11,13,19,22,26,38,143,209,247,286,418,494,2717,5434
Greatest Common Factor
We found the factors 8175,5434 . The biggest common factor number is the GCF number.
So the greatest common factor 8175,5434 is 1.
Lets's calculate LCM of 540,7672
| 2 | 540, 7672 |
| 2 | 270, 3836 |
| 135, 1918 |
∴ So the LCM of the given numbers is 2 x 2 x 135 x 1918 = 1035720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1035720
Therefore, the GCF of Fractions 8175/540,5434/7672 is 1/1035720
Least Common Multiple of 540,7672 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 540,7672 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(540,7672) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(540,7672) x common factors =4 x 1 = 4
LCM(540,7672) = ( 540 × 7672 ) / 4
LCM(540,7672) = 4142880 / 4
LCM(540,7672) = 1035720
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FAQs on GCF of Fractions of 8175/540, 5434/7672
1. What is the HCF of 8175,5434?
The HCF of 8175,5434 is 1
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 8175/540, 5434/7672?
Answer: GCF of Numerators as per given numbers 8175/540, 5434/7672 is
GCF of Numerators i.e. for 8175,5434 is 1
LCM of denominators i.e. for 540,7672 is 1035720.
Thus, GCF of Fractions is 1/1035720.Finally, GCF of Fractions for 8175/540, 5434/7672 is 1/1035720.