GCF of 342/497, 9984/663
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 342/497, 9984/663 i.e 6/329511 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/497, 9984/663.
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 342/497,9984/663?
Given fractions are 342/497,9984/663
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 342/497,9984/663, numerators are 342,9984
Denominators are 497,663
The GCF of 342,9984 is 6 .
LCM of 497,663 is 329511.
The greatest common factor of 342/497,9984/663 = [GCF of 342,9984]/[LCM of 497,663]= 6/329511
Therefore, the GCF of 342/497,9984/663 is 6/329511.
To find the highest common factor of 342,9984, 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 9984 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984
The HCF of 342,9984 is 6.
Lets's calculate GCF of 342,9984
| 2 | 342, 9984 |
| 3 | 171, 4992 |
| 57, 1664 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 342,9984 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 9984
:1,2,3,4,6,8,12,13,16,24,26,32,39,48,52,64,78,96,104,128,156,192,208,256,312,384,416,624,768,832,1248,1664,2496,3328,4992,9984
Greatest Common Factor
We found the factors 342,9984 . The biggest common factor number is the GCF number.
So the greatest common factor 342,9984 is 6.
Lets's calculate LCM of 497,663
Given numbers has no common factors except 1. So, there LCM is their product i.e 329511
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/329511
Therefore, the GCF of Fractions 342/497,9984/663 is 6/329511
Least Common Multiple of 497,663 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 497,663 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(497,663) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(497,663) x common factors =1 x 1 = 1
LCM(497,663) = ( 497 × 663 ) / 1
LCM(497,663) = 329511 / 1
LCM(497,663) = 329511
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FAQs on GCF of Fractions of 342/497, 9984/663
1. What is the HCF of 342,9984?
The HCF of 342,9984 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 342/497, 9984/663?
Answer: GCF of Numerators as per given numbers 342/497, 9984/663 is
GCF of Numerators i.e. for 342,9984 is 6
LCM of denominators i.e. for 497,663 is 329511.
Thus, GCF of Fractions is 6/329511.Finally, GCF of Fractions for 342/497, 9984/663 is 6/329511.