GCF of 50/60, 38/21, 25/77, 72/680
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 50/60, 38/21, 25/77, 72/680 i.e 1/157080 easily. The following is the detailed procedure to determine the greatest common factor of fractions 50/60, 38/21, 25/77, 72/680.
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 50/60,38/21,25/77,72/680?
Given fractions are 50/60,38/21,25/77,72/680
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 50/60,38/21,25/77,72/680, numerators are 50,38,25,72
Denominators are 60,21,77,680
The GCF of 50,38,25,72 is 1 .
LCM of 60,21,77,680 is 157080.
The greatest common factor of 50/60,38/21,25/77,72/680 = [GCF of 50,38,25,72]/[LCM of 60,21,77,680]= 1/157080
Therefore, the GCF of 50/60,38/21,25/77,72/680 is 1/157080.
To find the highest common factor of 50,38,25,72, we have to find the factors of both numbers and list the highest common factor.
The factors of 50 are 1, 2, 5, 10, 25, 50
The factors of 38 are 1, 2, 19, 38
The factors of 25 are 1, 5, 25
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The HCF of 50,38,25,72 is 1.
Lets's calculate GCF of 50,38,25,72
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 50,38,25,72 By Matching Biggest Common Factor Method
Now, list down the factors of 50
:1,2,5,10,25,50
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 25
:1,5,25
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Greatest Common Factor
We found the factors 50,38,25,72 . The biggest common factor number is the GCF number.
So the greatest common factor 50,38,25,72 is 1.
Lets's calculate LCM of 60,21,77,680
| 2 | 60, 21, 77, 680 |
| 2 | 30, 21, 77, 340 |
| 3 | 15, 21, 77, 170 |
| 5 | 5, 7, 77, 170 |
| 7 | 1, 7, 77, 34 |
| 1, 1, 11, 34 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 1 x 1 x 11 x 34 = 157080
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/157080
Therefore, the GCF of Fractions 50/60,38/21,25/77,72/680 is 1/157080
Least Common Multiple of 60,21,77,680 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 60,21,77,680 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,21,77,680) = 1
common factors(in case of two or more numbers have common factors) = 420
GCF(60,21,77,680) x common factors =1 x 420 = 420
LCM(60,21,77,680) = ( 60 × 21 × 77 × 680 ) / 420
LCM(60,21,77,680) = 65973600 / 420
LCM(60,21,77,680) = 157080
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 50/60, 38/21, 25/77, 72/680
1. What is the HCF of 50,38,25,72?
The HCF of 50,38,25,72 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 50/60, 38/21, 25/77, 72/680?
Answer: GCF of Numerators as per given numbers 50/60, 38/21, 25/77, 72/680 is
GCF of Numerators i.e. for 50,38,25,72 is 1
LCM of denominators i.e. for 60,21,77,680 is 157080.
Thus, GCF of Fractions is 1/157080.Finally, GCF of Fractions for 50/60, 38/21, 25/77, 72/680 is 1/157080.