GCF of 14/65, 26/78, 26/66, 74/675
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 14/65, 26/78, 26/66, 74/675 i.e 2/193050 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/65, 26/78, 26/66, 74/675.
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 14/65,26/78,26/66,74/675?
Given fractions are 14/65,26/78,26/66,74/675
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 14/65,26/78,26/66,74/675, numerators are 14,26,26,74
Denominators are 65,78,66,675
The GCF of 14,26,26,74 is 2 .
LCM of 65,78,66,675 is 193050.
The greatest common factor of 14/65,26/78,26/66,74/675 = [GCF of 14,26,26,74]/[LCM of 65,78,66,675]= 2/193050
Therefore, the GCF of 14/65,26/78,26/66,74/675 is 2/193050.
To find the highest common factor of 14,26,26,74, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 26 are 1, 2, 13, 26
The factors of 26 are 1, 2, 13, 26
The factors of 74 are 1, 2, 37, 74
The HCF of 14,26,26,74 is 2.
Lets's calculate GCF of 14,26,26,74
| 2 | 14, 26, 26, 74 |
| 7, 13, 13, 37 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 14,26,26,74 By Matching Biggest Common Factor Method
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 26
:1,2,13,26
Now, list down the factors of 26
:1,2,13,26
Now, list down the factors of 74
:1,2,37,74
Greatest Common Factor
We found the factors 14,26,26,74 . The biggest common factor number is the GCF number.
So the greatest common factor 14,26,26,74 is 2.
Lets's calculate LCM of 65,78,66,675
| 2 | 65, 78, 66, 675 |
| 3 | 65, 39, 33, 675 |
| 5 | 65, 13, 11, 225 |
| 13 | 13, 13, 11, 45 |
| 1, 1, 11, 45 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 1 x 1 x 11 x 45 = 193050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/193050
Therefore, the GCF of Fractions 14/65,26/78,26/66,74/675 is 2/193050
Least Common Multiple of 65,78,66,675 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 65,78,66,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,78,66,675) = 1
common factors(in case of two or more numbers have common factors) = 1170
GCF(65,78,66,675) x common factors =1 x 1170 = 1170
LCM(65,78,66,675) = ( 65 × 78 × 66 × 675 ) / 1170
LCM(65,78,66,675) = 225868500 / 1170
LCM(65,78,66,675) = 193050
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 14/65, 26/78, 26/66, 74/675
1. What is the HCF of 14,26,26,74?
The HCF of 14,26,26,74 is 2
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 14/65, 26/78, 26/66, 74/675?
Answer: GCF of Numerators as per given numbers 14/65, 26/78, 26/66, 74/675 is
GCF of Numerators i.e. for 14,26,26,74 is 2
LCM of denominators i.e. for 65,78,66,675 is 193050.
Thus, GCF of Fractions is 2/193050.Finally, GCF of Fractions for 14/65, 26/78, 26/66, 74/675 is 2/193050.