GCF of 172/40, 129/584
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 172/40, 129/584 i.e 43/2920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/40, 129/584.
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 172/40,129/584?
Given fractions are 172/40,129/584
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 172/40,129/584, numerators are 172,129
Denominators are 40,584
The GCF of 172,129 is 43 .
LCM of 40,584 is 2920.
The greatest common factor of 172/40,129/584 = [GCF of 172,129]/[LCM of 40,584]= 43/2920
Therefore, the GCF of 172/40,129/584 is 43/2920.
To find the highest common factor of 172,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 172 are 1, 2, 4, 43, 86, 172
The factors of 129 are 1, 3, 43, 129
The HCF of 172,129 is 43.
Lets's calculate GCF of 172,129
| 43 | 172, 129 |
| 4, 3 |
∴ So the GCF of the given numbers is 43 = 43
Greatest Common Factor of 172,129 By Matching Biggest Common Factor Method
Now, list down the factors of 172
:1,2,4,43,86,172
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 172,129 . The biggest common factor number is the GCF number.
So the greatest common factor 172,129 is 43.
Lets's calculate LCM of 40,584
| 2 | 40, 584 |
| 2 | 20, 292 |
| 2 | 10, 146 |
| 5, 73 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 73 = 2920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 43/2920
Therefore, the GCF of Fractions 172/40,129/584 is 43/2920
Least Common Multiple of 40,584 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 40,584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,584) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(40,584) x common factors =8 x 1 = 8
LCM(40,584) = ( 40 × 584 ) / 8
LCM(40,584) = 23360 / 8
LCM(40,584) = 2920
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FAQs on GCF of Fractions of 172/40, 129/584
1. What is the HCF of 172,129?
The HCF of 172,129 is 43
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 172/40, 129/584?
Answer: GCF of Numerators as per given numbers 172/40, 129/584 is
GCF of Numerators i.e. for 172,129 is 43
LCM of denominators i.e. for 40,584 is 2920.
Thus, GCF of Fractions is 43/2920.Finally, GCF of Fractions for 172/40, 129/584 is 43/2920.