GCF of 21/180, 66/280, 854/280
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/180, 66/280, 854/280 i.e 1/2520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/180, 66/280, 854/280.
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 21/180,66/280,854/280?
Given fractions are 21/180,66/280,854/280
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 21/180,66/280,854/280, numerators are 21,66,854
Denominators are 180,280,280
The GCF of 21,66,854 is 1 .
LCM of 180,280,280 is 2520.
The greatest common factor of 21/180,66/280,854/280 = [GCF of 21,66,854]/[LCM of 180,280,280]= 1/2520
Therefore, the GCF of 21/180,66/280,854/280 is 1/2520.
To find the highest common factor of 21,66,854, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The HCF of 21,66,854 is 1.
Lets's calculate GCF of 21,66,854
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,66,854 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Greatest Common Factor
We found the factors 21,66,854 . The biggest common factor number is the GCF number.
So the greatest common factor 21,66,854 is 1.
Lets's calculate LCM of 180,280,280
| 2 | 180, 280, 280 |
| 2 | 90, 140, 140 |
| 2 | 45, 70, 70 |
| 5 | 45, 35, 35 |
| 7 | 9, 7, 7 |
| 9, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 7 x 9 x 1 x 1 = 2520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2520
Therefore, the GCF of Fractions 21/180,66/280,854/280 is 1/2520
Least Common Multiple of 180,280,280 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 180,280,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,280,280) = 20
common factors(in case of two or more numbers have common factors) = 280
GCF(180,280,280) x common factors =20 x 280 = 5600
LCM(180,280,280) = ( 180 × 280 × 280 ) / 5600
LCM(180,280,280) = 14112000 / 5600
LCM(180,280,280) = 2520
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 21/180, 66/280, 854/280
1. What is the HCF of 21,66,854?
The HCF of 21,66,854 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 21/180, 66/280, 854/280?
Answer: GCF of Numerators as per given numbers 21/180, 66/280, 854/280 is
GCF of Numerators i.e. for 21,66,854 is 1
LCM of denominators i.e. for 180,280,280 is 2520.
Thus, GCF of Fractions is 1/2520.Finally, GCF of Fractions for 21/180, 66/280, 854/280 is 1/2520.