GCF of 108/312, 6948/235
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 108/312, 6948/235 i.e 36/73320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/312, 6948/235.
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 108/312,6948/235?
Given fractions are 108/312,6948/235
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 108/312,6948/235, numerators are 108,6948
Denominators are 312,235
The GCF of 108,6948 is 36 .
LCM of 312,235 is 73320.
The greatest common factor of 108/312,6948/235 = [GCF of 108,6948]/[LCM of 312,235]= 36/73320
Therefore, the GCF of 108/312,6948/235 is 36/73320.
To find the highest common factor of 108,6948, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 6948 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 193, 386, 579, 772, 1158, 1737, 2316, 3474, 6948
The HCF of 108,6948 is 36.
Lets's calculate GCF of 108,6948
| 2 | 108, 6948 |
| 2 | 54, 3474 |
| 3 | 27, 1737 |
| 3 | 9, 579 |
| 3, 193 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 3 = 36
Greatest Common Factor of 108,6948 By Matching Biggest Common Factor Method
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 6948
:1,2,3,4,6,9,12,18,36,193,386,579,772,1158,1737,2316,3474,6948
Greatest Common Factor
We found the factors 108,6948 . The biggest common factor number is the GCF number.
So the greatest common factor 108,6948 is 36.
Lets's calculate LCM of 312,235
Given numbers has no common factors except 1. So, there LCM is their product i.e 73320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 36/73320
Therefore, the GCF of Fractions 108/312,6948/235 is 36/73320
Least Common Multiple of 312,235 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 312,235 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,235) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(312,235) x common factors =1 x 1 = 1
LCM(312,235) = ( 312 × 235 ) / 1
LCM(312,235) = 73320 / 1
LCM(312,235) = 73320
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FAQs on GCF of Fractions of 108/312, 6948/235
1. What is the HCF of 108,6948?
The HCF of 108,6948 is 36
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 108/312, 6948/235?
Answer: GCF of Numerators as per given numbers 108/312, 6948/235 is
GCF of Numerators i.e. for 108,6948 is 36
LCM of denominators i.e. for 312,235 is 73320.
Thus, GCF of Fractions is 36/73320.Finally, GCF of Fractions for 108/312, 6948/235 is 36/73320.