GCF of 49/208, 51/464, 600/130
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 49/208, 51/464, 600/130 i.e 1/30160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/208, 51/464, 600/130.
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 49/208,51/464,600/130?
Given fractions are 49/208,51/464,600/130
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 49/208,51/464,600/130, numerators are 49,51,600
Denominators are 208,464,130
The GCF of 49,51,600 is 1 .
LCM of 208,464,130 is 30160.
The greatest common factor of 49/208,51/464,600/130 = [GCF of 49,51,600]/[LCM of 208,464,130]= 1/30160
Therefore, the GCF of 49/208,51/464,600/130 is 1/30160.
To find the highest common factor of 49,51,600, we have to find the factors of both numbers and list the highest common factor.
The factors of 49 are 1, 7, 49
The factors of 51 are 1, 3, 17, 51
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The HCF of 49,51,600 is 1.
Lets's calculate GCF of 49,51,600
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 49,51,600 By Matching Biggest Common Factor Method
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 51
:1,3,17,51
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Greatest Common Factor
We found the factors 49,51,600 . The biggest common factor number is the GCF number.
So the greatest common factor 49,51,600 is 1.
Lets's calculate LCM of 208,464,130
| 2 | 208, 464, 130 |
| 2 | 104, 232, 65 |
| 2 | 52, 116, 65 |
| 2 | 26, 58, 65 |
| 13 | 13, 29, 65 |
| 1, 29, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 13 x 1 x 29 x 5 = 30160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30160
Therefore, the GCF of Fractions 49/208,51/464,600/130 is 1/30160
Least Common Multiple of 208,464,130 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 208,464,130 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,464,130) = 2
common factors(in case of two or more numbers have common factors) = 208
GCF(208,464,130) x common factors =2 x 208 = 416
LCM(208,464,130) = ( 208 × 464 × 130 ) / 416
LCM(208,464,130) = 12546560 / 416
LCM(208,464,130) = 30160
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 49/208, 51/464, 600/130
1. What is the HCF of 49,51,600?
The HCF of 49,51,600 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 49/208, 51/464, 600/130?
Answer: GCF of Numerators as per given numbers 49/208, 51/464, 600/130 is
GCF of Numerators i.e. for 49,51,600 is 1
LCM of denominators i.e. for 208,464,130 is 30160.
Thus, GCF of Fractions is 1/30160.Finally, GCF of Fractions for 49/208, 51/464, 600/130 is 1/30160.