GCF of 8142/71, 5622/584
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8142/71, 5622/584 i.e 6/41464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8142/71, 5622/584.
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 8142/71,5622/584?
Given fractions are 8142/71,5622/584
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 8142/71,5622/584, numerators are 8142,5622
Denominators are 71,584
The GCF of 8142,5622 is 6 .
LCM of 71,584 is 41464.
The greatest common factor of 8142/71,5622/584 = [GCF of 8142,5622]/[LCM of 71,584]= 6/41464
Therefore, the GCF of 8142/71,5622/584 is 6/41464.
To find the highest common factor of 8142,5622, we have to find the factors of both numbers and list the highest common factor.
The factors of 8142 are 1, 2, 3, 6, 23, 46, 59, 69, 118, 138, 177, 354, 1357, 2714, 4071, 8142
The factors of 5622 are 1, 2, 3, 6, 937, 1874, 2811, 5622
The HCF of 8142,5622 is 6.
Lets's calculate GCF of 8142,5622
| 2 | 8142, 5622 |
| 3 | 4071, 2811 |
| 1357, 937 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 8142,5622 By Matching Biggest Common Factor Method
Now, list down the factors of 8142
:1,2,3,6,23,46,59,69,118,138,177,354,1357,2714,4071,8142
Now, list down the factors of 5622
:1,2,3,6,937,1874,2811,5622
Greatest Common Factor
We found the factors 8142,5622 . The biggest common factor number is the GCF number.
So the greatest common factor 8142,5622 is 6.
Lets's calculate LCM of 71,584
Given numbers has no common factors except 1. So, there LCM is their product i.e 41464
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/41464
Therefore, the GCF of Fractions 8142/71,5622/584 is 6/41464
Least Common Multiple of 71,584 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 71,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,584) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(71,584) x common factors =1 x 1 = 1
LCM(71,584) = ( 71 × 584 ) / 1
LCM(71,584) = 41464 / 1
LCM(71,584) = 41464
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FAQs on GCF of Fractions of 8142/71, 5622/584
1. What is the HCF of 8142,5622?
The HCF of 8142,5622 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 8142/71, 5622/584?
Answer: GCF of Numerators as per given numbers 8142/71, 5622/584 is
GCF of Numerators i.e. for 8142,5622 is 6
LCM of denominators i.e. for 71,584 is 41464.
Thus, GCF of Fractions is 6/41464.Finally, GCF of Fractions for 8142/71, 5622/584 is 6/41464.