GCF of 343/49, 882/6240
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 343/49, 882/6240 i.e 49/305760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 343/49, 882/6240.
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 343/49,882/6240?
Given fractions are 343/49,882/6240
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 343/49,882/6240, numerators are 343,882
Denominators are 49,6240
The GCF of 343,882 is 49 .
LCM of 49,6240 is 305760.
The greatest common factor of 343/49,882/6240 = [GCF of 343,882]/[LCM of 49,6240]= 49/305760
Therefore, the GCF of 343/49,882/6240 is 49/305760.
To find the highest common factor of 343,882, we have to find the factors of both numbers and list the highest common factor.
The factors of 343 are 1, 7, 49, 343
The factors of 882 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882
The HCF of 343,882 is 49.
Lets's calculate GCF of 343,882
| 7 | 343, 882 |
| 7 | 49, 126 |
| 7, 18 |
∴ So the GCF of the given numbers is 7 x 7 = 49
Greatest Common Factor of 343,882 By Matching Biggest Common Factor Method
Now, list down the factors of 343
:1,7,49,343
Now, list down the factors of 882
:1,2,3,6,7,9,14,18,21,42,49,63,98,126,147,294,441,882
Greatest Common Factor
We found the factors 343,882 . The biggest common factor number is the GCF number.
So the greatest common factor 343,882 is 49.
Lets's calculate LCM of 49,6240
Given numbers has no common factors except 1. So, there LCM is their product i.e 305760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 49/305760
Therefore, the GCF of Fractions 343/49,882/6240 is 49/305760
Least Common Multiple of 49,6240 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 49,6240 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(49,6240) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(49,6240) x common factors =1 x 1 = 1
LCM(49,6240) = ( 49 × 6240 ) / 1
LCM(49,6240) = 305760 / 1
LCM(49,6240) = 305760
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FAQs on GCF of Fractions of 343/49, 882/6240
1. What is the HCF of 343,882?
The HCF of 343,882 is 49
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 343/49, 882/6240?
Answer: GCF of Numerators as per given numbers 343/49, 882/6240 is
GCF of Numerators i.e. for 343,882 is 49
LCM of denominators i.e. for 49,6240 is 305760.
Thus, GCF of Fractions is 49/305760.Finally, GCF of Fractions for 343/49, 882/6240 is 49/305760.