GCF of 4/67, 14/84, 36/277, 272/721
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4/67, 14/84, 36/277, 272/721 i.e 2/160572468 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4/67, 14/84, 36/277, 272/721.
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 4/67,14/84,36/277,272/721?
Given fractions are 4/67,14/84,36/277,272/721
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 4/67,14/84,36/277,272/721, numerators are 4,14,36,272
Denominators are 67,84,277,721
The GCF of 4,14,36,272 is 2 .
LCM of 67,84,277,721 is 160572468.
The greatest common factor of 4/67,14/84,36/277,272/721 = [GCF of 4,14,36,272]/[LCM of 67,84,277,721]= 2/160572468
Therefore, the GCF of 4/67,14/84,36/277,272/721 is 2/160572468.
To find the highest common factor of 4,14,36,272, we have to find the factors of both numbers and list the highest common factor.
The factors of 4 are 1, 2, 4
The factors of 14 are 1, 2, 7, 14
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
The HCF of 4,14,36,272 is 2.
Lets's calculate GCF of 4,14,36,272
| 2 | 4, 14, 36, 272 |
| 2, 7, 18, 136 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4,14,36,272 By Matching Biggest Common Factor Method
Now, list down the factors of 4
:1,2,4
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
Greatest Common Factor
We found the factors 4,14,36,272 . The biggest common factor number is the GCF number.
So the greatest common factor 4,14,36,272 is 2.
Lets's calculate LCM of 67,84,277,721
| 7 | 67, 84, 277, 721 |
| 67, 12, 277, 103 |
∴ So the LCM of the given numbers is 7 x 67 x 12 x 277 x 103 = 160572468
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/160572468
Therefore, the GCF of Fractions 4/67,14/84,36/277,272/721 is 2/160572468
Least Common Multiple of 67,84,277,721 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 67,84,277,721 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,84,277,721) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(67,84,277,721) x common factors =1 x 7 = 7
LCM(67,84,277,721) = ( 67 × 84 × 277 × 721 ) / 7
LCM(67,84,277,721) = 1124007276 / 7
LCM(67,84,277,721) = 160572468
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 4/67, 14/84, 36/277, 272/721
1. What is the HCF of 4,14,36,272?
The HCF of 4,14,36,272 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 4/67, 14/84, 36/277, 272/721?
Answer: GCF of Numerators as per given numbers 4/67, 14/84, 36/277, 272/721 is
GCF of Numerators i.e. for 4,14,36,272 is 2
LCM of denominators i.e. for 67,84,277,721 is 160572468.
Thus, GCF of Fractions is 2/160572468.Finally, GCF of Fractions for 4/67, 14/84, 36/277, 272/721 is 2/160572468.