GCF of 3416/724, 3920/3098
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3416/724, 3920/3098 i.e 56/1121476 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3416/724, 3920/3098.
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 3416/724,3920/3098?
Given fractions are 3416/724,3920/3098
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 3416/724,3920/3098, numerators are 3416,3920
Denominators are 724,3098
The GCF of 3416,3920 is 56 .
LCM of 724,3098 is 1121476.
The greatest common factor of 3416/724,3920/3098 = [GCF of 3416,3920]/[LCM of 724,3098]= 56/1121476
Therefore, the GCF of 3416/724,3920/3098 is 56/1121476.
To find the highest common factor of 3416,3920, we have to find the factors of both numbers and list the highest common factor.
The factors of 3416 are 1, 2, 4, 7, 8, 14, 28, 56, 61, 122, 244, 427, 488, 854, 1708, 3416
The factors of 3920 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 49, 56, 70, 80, 98, 112, 140, 196, 245, 280, 392, 490, 560, 784, 980, 1960, 3920
The HCF of 3416,3920 is 56.
Lets's calculate GCF of 3416,3920
| 2 | 3416, 3920 |
| 2 | 1708, 1960 |
| 2 | 854, 980 |
| 7 | 427, 490 |
| 61, 70 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56
Greatest Common Factor of 3416,3920 By Matching Biggest Common Factor Method
Now, list down the factors of 3416
:1,2,4,7,8,14,28,56,61,122,244,427,488,854,1708,3416
Now, list down the factors of 3920
:1,2,4,5,7,8,10,14,16,20,28,35,40,49,56,70,80,98,112,140,196,245,280,392,490,560,784,980,1960,3920
Greatest Common Factor
We found the factors 3416,3920 . The biggest common factor number is the GCF number.
So the greatest common factor 3416,3920 is 56.
Lets's calculate LCM of 724,3098
| 2 | 724, 3098 |
| 362, 1549 |
∴ So the LCM of the given numbers is 2 x 362 x 1549 = 1121476
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/1121476
Therefore, the GCF of Fractions 3416/724,3920/3098 is 56/1121476
Least Common Multiple of 724,3098 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 724,3098 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(724,3098) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(724,3098) x common factors =2 x 1 = 2
LCM(724,3098) = ( 724 × 3098 ) / 2
LCM(724,3098) = 2242952 / 2
LCM(724,3098) = 1121476
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3416/724, 3920/3098
1. What is the HCF of 3416,3920?
The HCF of 3416,3920 is 56
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 3416/724, 3920/3098?
Answer: GCF of Numerators as per given numbers 3416/724, 3920/3098 is
GCF of Numerators i.e. for 3416,3920 is 56
LCM of denominators i.e. for 724,3098 is 1121476.
Thus, GCF of Fractions is 56/1121476.Finally, GCF of Fractions for 3416/724, 3920/3098 is 56/1121476.