GCF of 120/682, 3136/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 120/682, 3136/319 i.e 8/19778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/682, 3136/319.
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 120/682,3136/319?
Given fractions are 120/682,3136/319
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 120/682,3136/319, numerators are 120,3136
Denominators are 682,319
The GCF of 120,3136 is 8 .
LCM of 682,319 is 19778.
The greatest common factor of 120/682,3136/319 = [GCF of 120,3136]/[LCM of 682,319]= 8/19778
Therefore, the GCF of 120/682,3136/319 is 8/19778.
To find the highest common factor of 120,3136, we have to find the factors of both numbers and list the highest common factor.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 3136 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 196, 224, 392, 448, 784, 1568, 3136
The HCF of 120,3136 is 8.
Lets's calculate GCF of 120,3136
| 2 | 120, 3136 |
| 2 | 60, 1568 |
| 2 | 30, 784 |
| 15, 392 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 120,3136 By Matching Biggest Common Factor Method
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Now, list down the factors of 3136
:1,2,4,7,8,14,16,28,32,49,56,64,98,112,196,224,392,448,784,1568,3136
Greatest Common Factor
We found the factors 120,3136 . The biggest common factor number is the GCF number.
So the greatest common factor 120,3136 is 8.
Lets's calculate LCM of 682,319
| 11 | 682, 319 |
| 62, 29 |
∴ So the LCM of the given numbers is 11 x 62 x 29 = 19778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/19778
Therefore, the GCF of Fractions 120/682,3136/319 is 8/19778
Least Common Multiple of 682,319 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 682,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(682,319) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(682,319) x common factors =11 x 1 = 11
LCM(682,319) = ( 682 × 319 ) / 11
LCM(682,319) = 217558 / 11
LCM(682,319) = 19778
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FAQs on GCF of Fractions of 120/682, 3136/319
1. What is the HCF of 120,3136?
The HCF of 120,3136 is 8
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 120/682, 3136/319?
Answer: GCF of Numerators as per given numbers 120/682, 3136/319 is
GCF of Numerators i.e. for 120,3136 is 8
LCM of denominators i.e. for 682,319 is 19778.
Thus, GCF of Fractions is 8/19778.Finally, GCF of Fractions for 120/682, 3136/319 is 8/19778.