GCF of 9/67, 52/46, 75/265, 137/212
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9/67, 52/46, 75/265, 137/212 i.e 1/1633460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9/67, 52/46, 75/265, 137/212.
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 9/67,52/46,75/265,137/212?
Given fractions are 9/67,52/46,75/265,137/212
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 9/67,52/46,75/265,137/212, numerators are 9,52,75,137
Denominators are 67,46,265,212
The GCF of 9,52,75,137 is 1 .
LCM of 67,46,265,212 is 1633460.
The greatest common factor of 9/67,52/46,75/265,137/212 = [GCF of 9,52,75,137]/[LCM of 67,46,265,212]= 1/1633460
Therefore, the GCF of 9/67,52/46,75/265,137/212 is 1/1633460.
To find the highest common factor of 9,52,75,137, we have to find the factors of both numbers and list the highest common factor.
The factors of 9 are 1, 3, 9
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 137 are 1, 137
The HCF of 9,52,75,137 is 1.
Lets's calculate GCF of 9,52,75,137
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 9,52,75,137 By Matching Biggest Common Factor Method
Now, list down the factors of 9
:1,3,9
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 137
:1,137
Greatest Common Factor
We found the factors 9,52,75,137 . The biggest common factor number is the GCF number.
So the greatest common factor 9,52,75,137 is 1.
Lets's calculate LCM of 67,46,265,212
| 2 | 67, 46, 265, 212 |
| 53 | 67, 23, 265, 106 |
| 67, 23, 5, 2 |
∴ So the LCM of the given numbers is 2 x 53 x 67 x 23 x 5 x 2 = 1633460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1633460
Therefore, the GCF of Fractions 9/67,52/46,75/265,137/212 is 1/1633460
Least Common Multiple of 67,46,265,212 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 67,46,265,212 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,46,265,212) = 1
common factors(in case of two or more numbers have common factors) = 106
GCF(67,46,265,212) x common factors =1 x 106 = 106
LCM(67,46,265,212) = ( 67 × 46 × 265 × 212 ) / 106
LCM(67,46,265,212) = 173146760 / 106
LCM(67,46,265,212) = 1633460
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 9/67, 52/46, 75/265, 137/212
1. What is the HCF of 9,52,75,137?
The HCF of 9,52,75,137 is 1
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 9/67, 52/46, 75/265, 137/212?
Answer: GCF of Numerators as per given numbers 9/67, 52/46, 75/265, 137/212 is
GCF of Numerators i.e. for 9,52,75,137 is 1
LCM of denominators i.e. for 67,46,265,212 is 1633460.
Thus, GCF of Fractions is 1/1633460.Finally, GCF of Fractions for 9/67, 52/46, 75/265, 137/212 is 1/1633460.