GCF of 3454/680, 6894/2068
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3454/680, 6894/2068 i.e 2/351560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3454/680, 6894/2068.
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 3454/680,6894/2068?
Given fractions are 3454/680,6894/2068
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 3454/680,6894/2068, numerators are 3454,6894
Denominators are 680,2068
The GCF of 3454,6894 is 2 .
LCM of 680,2068 is 351560.
The greatest common factor of 3454/680,6894/2068 = [GCF of 3454,6894]/[LCM of 680,2068]= 2/351560
Therefore, the GCF of 3454/680,6894/2068 is 2/351560.
To find the highest common factor of 3454,6894, we have to find the factors of both numbers and list the highest common factor.
The factors of 3454 are 1, 2, 11, 22, 157, 314, 1727, 3454
The factors of 6894 are 1, 2, 3, 6, 9, 18, 383, 766, 1149, 2298, 3447, 6894
The HCF of 3454,6894 is 2.
Lets's calculate GCF of 3454,6894
| 2 | 3454, 6894 |
| 1727, 3447 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3454,6894 By Matching Biggest Common Factor Method
Now, list down the factors of 3454
:1,2,11,22,157,314,1727,3454
Now, list down the factors of 6894
:1,2,3,6,9,18,383,766,1149,2298,3447,6894
Greatest Common Factor
We found the factors 3454,6894 . The biggest common factor number is the GCF number.
So the greatest common factor 3454,6894 is 2.
Lets's calculate LCM of 680,2068
| 2 | 680, 2068 |
| 2 | 340, 1034 |
| 170, 517 |
∴ So the LCM of the given numbers is 2 x 2 x 170 x 517 = 351560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/351560
Therefore, the GCF of Fractions 3454/680,6894/2068 is 2/351560
Least Common Multiple of 680,2068 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 680,2068 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(680,2068) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(680,2068) x common factors =4 x 1 = 4
LCM(680,2068) = ( 680 × 2068 ) / 4
LCM(680,2068) = 1406240 / 4
LCM(680,2068) = 351560
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FAQs on GCF of Fractions of 3454/680, 6894/2068
1. What is the HCF of 3454,6894?
The HCF of 3454,6894 is 2
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 3454/680, 6894/2068?
Answer: GCF of Numerators as per given numbers 3454/680, 6894/2068 is
GCF of Numerators i.e. for 3454,6894 is 2
LCM of denominators i.e. for 680,2068 is 351560.
Thus, GCF of Fractions is 2/351560.Finally, GCF of Fractions for 3454/680, 6894/2068 is 2/351560.