GCF of 171/26, 972/169
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 171/26, 972/169 i.e 9/338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 171/26, 972/169.
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 171/26,972/169?
Given fractions are 171/26,972/169
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 171/26,972/169, numerators are 171,972
Denominators are 26,169
The GCF of 171,972 is 9 .
LCM of 26,169 is 338.
The greatest common factor of 171/26,972/169 = [GCF of 171,972]/[LCM of 26,169]= 9/338
Therefore, the GCF of 171/26,972/169 is 9/338.
To find the highest common factor of 171,972, we have to find the factors of both numbers and list the highest common factor.
The factors of 171 are 1, 3, 9, 19, 57, 171
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The HCF of 171,972 is 9.
Lets's calculate GCF of 171,972
| 3 | 171, 972 |
| 3 | 57, 324 |
| 19, 108 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 171,972 By Matching Biggest Common Factor Method
Now, list down the factors of 171
:1,3,9,19,57,171
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Greatest Common Factor
We found the factors 171,972 . The biggest common factor number is the GCF number.
So the greatest common factor 171,972 is 9.
Lets's calculate LCM of 26,169
| 13 | 26, 169 |
| 2, 13 |
∴ So the LCM of the given numbers is 13 x 2 x 13 = 338
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/338
Therefore, the GCF of Fractions 171/26,972/169 is 9/338
Least Common Multiple of 26,169 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 26,169 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,169) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(26,169) x common factors =13 x 1 = 13
LCM(26,169) = ( 26 × 169 ) / 13
LCM(26,169) = 4394 / 13
LCM(26,169) = 338
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FAQs on GCF of Fractions of 171/26, 972/169
1. What is the HCF of 171,972?
The HCF of 171,972 is 9
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 171/26, 972/169?
Answer: GCF of Numerators as per given numbers 171/26, 972/169 is
GCF of Numerators i.e. for 171,972 is 9
LCM of denominators i.e. for 26,169 is 338.
Thus, GCF of Fractions is 9/338.Finally, GCF of Fractions for 171/26, 972/169 is 9/338.