GCF of 172/35, 860/125
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 172/35, 860/125 i.e 172/875 easily. The following is the detailed procedure to determine the greatest common factor of fractions 172/35, 860/125.
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 172/35,860/125?
Given fractions are 172/35,860/125
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 172/35,860/125, numerators are 172,860
Denominators are 35,125
The GCF of 172,860 is 172 .
LCM of 35,125 is 875.
The greatest common factor of 172/35,860/125 = [GCF of 172,860]/[LCM of 35,125]= 172/875
Therefore, the GCF of 172/35,860/125 is 172/875.
To find the highest common factor of 172,860, 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 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
The HCF of 172,860 is 172.
Lets's calculate GCF of 172,860
| 2 | 172, 860 |
| 2 | 86, 430 |
| 43 | 43, 215 |
| 1, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 43 = 172
Greatest Common Factor of 172,860 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 860
:1,2,4,5,10,20,43,86,172,215,430,860
Greatest Common Factor
We found the factors 172,860 . The biggest common factor number is the GCF number.
So the greatest common factor 172,860 is 172.
Lets's calculate LCM of 35,125
| 5 | 35, 125 |
| 7, 25 |
∴ So the LCM of the given numbers is 5 x 7 x 25 = 875
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 172/875
Therefore, the GCF of Fractions 172/35,860/125 is 172/875
Least Common Multiple of 35,125 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 35,125 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(35,125) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(35,125) x common factors =5 x 1 = 5
LCM(35,125) = ( 35 × 125 ) / 5
LCM(35,125) = 4375 / 5
LCM(35,125) = 875
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FAQs on GCF of Fractions of 172/35, 860/125
1. What is the HCF of 172,860?
The HCF of 172,860 is 172
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 172/35, 860/125?
Answer: GCF of Numerators as per given numbers 172/35, 860/125 is
GCF of Numerators i.e. for 172,860 is 172
LCM of denominators i.e. for 35,125 is 875.
Thus, GCF of Fractions is 172/875.Finally, GCF of Fractions for 172/35, 860/125 is 172/875.