GCF of 680/648, 5360/1334
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 680/648, 5360/1334 i.e 40/432216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/648, 5360/1334.
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 680/648,5360/1334?
Given fractions are 680/648,5360/1334
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 680/648,5360/1334, numerators are 680,5360
Denominators are 648,1334
The GCF of 680,5360 is 40 .
LCM of 648,1334 is 432216.
The greatest common factor of 680/648,5360/1334 = [GCF of 680,5360]/[LCM of 648,1334]= 40/432216
Therefore, the GCF of 680/648,5360/1334 is 40/432216.
To find the highest common factor of 680,5360, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 5360 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 67, 80, 134, 268, 335, 536, 670, 1072, 1340, 2680, 5360
The HCF of 680,5360 is 40.
Lets's calculate GCF of 680,5360
| 2 | 680, 5360 |
| 2 | 340, 2680 |
| 2 | 170, 1340 |
| 5 | 85, 670 |
| 17, 134 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 680,5360 By Matching Biggest Common Factor Method
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 5360
:1,2,4,5,8,10,16,20,40,67,80,134,268,335,536,670,1072,1340,2680,5360
Greatest Common Factor
We found the factors 680,5360 . The biggest common factor number is the GCF number.
So the greatest common factor 680,5360 is 40.
Lets's calculate LCM of 648,1334
| 2 | 648, 1334 |
| 324, 667 |
∴ So the LCM of the given numbers is 2 x 324 x 667 = 432216
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/432216
Therefore, the GCF of Fractions 680/648,5360/1334 is 40/432216
Least Common Multiple of 648,1334 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 648,1334 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(648,1334) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(648,1334) x common factors =2 x 1 = 2
LCM(648,1334) = ( 648 × 1334 ) / 2
LCM(648,1334) = 864432 / 2
LCM(648,1334) = 432216
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FAQs on GCF of Fractions of 680/648, 5360/1334
1. What is the HCF of 680,5360?
The HCF of 680,5360 is 40
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 680/648, 5360/1334?
Answer: GCF of Numerators as per given numbers 680/648, 5360/1334 is
GCF of Numerators i.e. for 680,5360 is 40
LCM of denominators i.e. for 648,1334 is 432216.
Thus, GCF of Fractions is 40/432216.Finally, GCF of Fractions for 680/648, 5360/1334 is 40/432216.