GCF of 342/640, 708/417
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/640, 708/417 i.e 6/266880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/640, 708/417.
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 342/640,708/417?
Given fractions are 342/640,708/417
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 342/640,708/417, numerators are 342,708
Denominators are 640,417
The GCF of 342,708 is 6 .
LCM of 640,417 is 266880.
The greatest common factor of 342/640,708/417 = [GCF of 342,708]/[LCM of 640,417]= 6/266880
Therefore, the GCF of 342/640,708/417 is 6/266880.
To find the highest common factor of 342,708, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
The HCF of 342,708 is 6.
Lets's calculate GCF of 342,708
| 2 | 342, 708 |
| 3 | 171, 354 |
| 57, 118 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 342,708 By Matching Biggest Common Factor Method
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 708
:1,2,3,4,6,12,59,118,177,236,354,708
Greatest Common Factor
We found the factors 342,708 . The biggest common factor number is the GCF number.
So the greatest common factor 342,708 is 6.
Lets's calculate LCM of 640,417
Given numbers has no common factors except 1. So, there LCM is their product i.e 266880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/266880
Therefore, the GCF of Fractions 342/640,708/417 is 6/266880
Least Common Multiple of 640,417 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 640,417 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(640,417) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(640,417) x common factors =1 x 1 = 1
LCM(640,417) = ( 640 × 417 ) / 1
LCM(640,417) = 266880 / 1
LCM(640,417) = 266880
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FAQs on GCF of Fractions of 342/640, 708/417
1. What is the HCF of 342,708?
The HCF of 342,708 is 6
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 342/640, 708/417?
Answer: GCF of Numerators as per given numbers 342/640, 708/417 is
GCF of Numerators i.e. for 342,708 is 6
LCM of denominators i.e. for 640,417 is 266880.
Thus, GCF of Fractions is 6/266880.Finally, GCF of Fractions for 342/640, 708/417 is 6/266880.