GCF of 142/174, 5309/669
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 142/174, 5309/669 i.e 1/38802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/174, 5309/669.
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 142/174,5309/669?
Given fractions are 142/174,5309/669
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 142/174,5309/669, numerators are 142,5309
Denominators are 174,669
The GCF of 142,5309 is 1 .
LCM of 174,669 is 38802.
The greatest common factor of 142/174,5309/669 = [GCF of 142,5309]/[LCM of 174,669]= 1/38802
Therefore, the GCF of 142/174,5309/669 is 1/38802.
To find the highest common factor of 142,5309, we have to find the factors of both numbers and list the highest common factor.
The factors of 142 are 1, 2, 71, 142
The factors of 5309 are 1, 5309
The HCF of 142,5309 is 1.
Lets's calculate GCF of 142,5309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 142,5309 By Matching Biggest Common Factor Method
Now, list down the factors of 142
:1,2,71,142
Now, list down the factors of 5309
:1,5309
Greatest Common Factor
We found the factors 142,5309 . The biggest common factor number is the GCF number.
So the greatest common factor 142,5309 is 1.
Lets's calculate LCM of 174,669
| 3 | 174, 669 |
| 58, 223 |
∴ So the LCM of the given numbers is 3 x 58 x 223 = 38802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/38802
Therefore, the GCF of Fractions 142/174,5309/669 is 1/38802
Least Common Multiple of 174,669 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 174,669 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,669) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(174,669) x common factors =3 x 1 = 3
LCM(174,669) = ( 174 × 669 ) / 3
LCM(174,669) = 116406 / 3
LCM(174,669) = 38802
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FAQs on GCF of Fractions of 142/174, 5309/669
1. What is the HCF of 142,5309?
The HCF of 142,5309 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 142/174, 5309/669?
Answer: GCF of Numerators as per given numbers 142/174, 5309/669 is
GCF of Numerators i.e. for 142,5309 is 1
LCM of denominators i.e. for 174,669 is 38802.
Thus, GCF of Fractions is 1/38802.Finally, GCF of Fractions for 142/174, 5309/669 is 1/38802.