GCF of 129/138, 1344/160
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 129/138, 1344/160 i.e 3/11040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 129/138, 1344/160.
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 129/138,1344/160?
Given fractions are 129/138,1344/160
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 129/138,1344/160, numerators are 129,1344
Denominators are 138,160
The GCF of 129,1344 is 3 .
LCM of 138,160 is 11040.
The greatest common factor of 129/138,1344/160 = [GCF of 129,1344]/[LCM of 138,160]= 3/11040
Therefore, the GCF of 129/138,1344/160 is 3/11040.
To find the highest common factor of 129,1344, we have to find the factors of both numbers and list the highest common factor.
The factors of 129 are 1, 3, 43, 129
The factors of 1344 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 168, 192, 224, 336, 448, 672, 1344
The HCF of 129,1344 is 3.
Lets's calculate GCF of 129,1344
| 3 | 129, 1344 |
| 43, 448 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 129,1344 By Matching Biggest Common Factor Method
Now, list down the factors of 129
:1,3,43,129
Now, list down the factors of 1344
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,56,64,84,96,112,168,192,224,336,448,672,1344
Greatest Common Factor
We found the factors 129,1344 . The biggest common factor number is the GCF number.
So the greatest common factor 129,1344 is 3.
Lets's calculate LCM of 138,160
| 2 | 138, 160 |
| 69, 80 |
∴ So the LCM of the given numbers is 2 x 69 x 80 = 11040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/11040
Therefore, the GCF of Fractions 129/138,1344/160 is 3/11040
Least Common Multiple of 138,160 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 138,160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(138,160) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(138,160) x common factors =2 x 1 = 2
LCM(138,160) = ( 138 × 160 ) / 2
LCM(138,160) = 22080 / 2
LCM(138,160) = 11040
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FAQs on GCF of Fractions of 129/138, 1344/160
1. What is the HCF of 129,1344?
The HCF of 129,1344 is 3
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 129/138, 1344/160?
Answer: GCF of Numerators as per given numbers 129/138, 1344/160 is
GCF of Numerators i.e. for 129,1344 is 3
LCM of denominators i.e. for 138,160 is 11040.
Thus, GCF of Fractions is 3/11040.Finally, GCF of Fractions for 129/138, 1344/160 is 3/11040.