GCF of 5170/74, 6171/172
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5170/74, 6171/172 i.e 11/6364 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5170/74, 6171/172.
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 5170/74,6171/172?
Given fractions are 5170/74,6171/172
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 5170/74,6171/172, numerators are 5170,6171
Denominators are 74,172
The GCF of 5170,6171 is 11 .
LCM of 74,172 is 6364.
The greatest common factor of 5170/74,6171/172 = [GCF of 5170,6171]/[LCM of 74,172]= 11/6364
Therefore, the GCF of 5170/74,6171/172 is 11/6364.
To find the highest common factor of 5170,6171, we have to find the factors of both numbers and list the highest common factor.
The factors of 5170 are 1, 2, 5, 10, 11, 22, 47, 55, 94, 110, 235, 470, 517, 1034, 2585, 5170
The factors of 6171 are 1, 3, 11, 17, 33, 51, 121, 187, 363, 561, 2057, 6171
The HCF of 5170,6171 is 11.
Lets's calculate GCF of 5170,6171
| 11 | 5170, 6171 |
| 470, 561 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 5170,6171 By Matching Biggest Common Factor Method
Now, list down the factors of 5170
:1,2,5,10,11,22,47,55,94,110,235,470,517,1034,2585,5170
Now, list down the factors of 6171
:1,3,11,17,33,51,121,187,363,561,2057,6171
Greatest Common Factor
We found the factors 5170,6171 . The biggest common factor number is the GCF number.
So the greatest common factor 5170,6171 is 11.
Lets's calculate LCM of 74,172
| 2 | 74, 172 |
| 37, 86 |
∴ So the LCM of the given numbers is 2 x 37 x 86 = 6364
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/6364
Therefore, the GCF of Fractions 5170/74,6171/172 is 11/6364
Least Common Multiple of 74,172 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 74,172 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,172) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,172) x common factors =2 x 1 = 2
LCM(74,172) = ( 74 × 172 ) / 2
LCM(74,172) = 12728 / 2
LCM(74,172) = 6364
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FAQs on GCF of Fractions of 5170/74, 6171/172
1. What is the HCF of 5170,6171?
The HCF of 5170,6171 is 11
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 5170/74, 6171/172?
Answer: GCF of Numerators as per given numbers 5170/74, 6171/172 is
GCF of Numerators i.e. for 5170,6171 is 11
LCM of denominators i.e. for 74,172 is 6364.
Thus, GCF of Fractions is 11/6364.Finally, GCF of Fractions for 5170/74, 6171/172 is 11/6364.