GCF of 1968/384, 4746/624
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1968/384, 4746/624 i.e 6/4992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1968/384, 4746/624.
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 1968/384,4746/624?
Given fractions are 1968/384,4746/624
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 1968/384,4746/624, numerators are 1968,4746
Denominators are 384,624
The GCF of 1968,4746 is 6 .
LCM of 384,624 is 4992.
The greatest common factor of 1968/384,4746/624 = [GCF of 1968,4746]/[LCM of 384,624]= 6/4992
Therefore, the GCF of 1968/384,4746/624 is 6/4992.
To find the highest common factor of 1968,4746, we have to find the factors of both numbers and list the highest common factor.
The factors of 1968 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968
The factors of 4746 are 1, 2, 3, 6, 7, 14, 21, 42, 113, 226, 339, 678, 791, 1582, 2373, 4746
The HCF of 1968,4746 is 6.
Lets's calculate GCF of 1968,4746
| 2 | 1968, 4746 |
| 3 | 984, 2373 |
| 328, 791 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1968,4746 By Matching Biggest Common Factor Method
Now, list down the factors of 1968
:1,2,3,4,6,8,12,16,24,41,48,82,123,164,246,328,492,656,984,1968
Now, list down the factors of 4746
:1,2,3,6,7,14,21,42,113,226,339,678,791,1582,2373,4746
Greatest Common Factor
We found the factors 1968,4746 . The biggest common factor number is the GCF number.
So the greatest common factor 1968,4746 is 6.
Lets's calculate LCM of 384,624
| 2 | 384, 624 |
| 2 | 192, 312 |
| 2 | 96, 156 |
| 2 | 48, 78 |
| 3 | 24, 39 |
| 8, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 8 x 13 = 4992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4992
Therefore, the GCF of Fractions 1968/384,4746/624 is 6/4992
Least Common Multiple of 384,624 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 384,624 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,624) = 48
common factors(in case of two or more numbers have common factors) = 1
GCF(384,624) x common factors =48 x 1 = 48
LCM(384,624) = ( 384 × 624 ) / 48
LCM(384,624) = 239616 / 48
LCM(384,624) = 4992
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FAQs on GCF of Fractions of 1968/384, 4746/624
1. What is the HCF of 1968,4746?
The HCF of 1968,4746 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 1968/384, 4746/624?
Answer: GCF of Numerators as per given numbers 1968/384, 4746/624 is
GCF of Numerators i.e. for 1968,4746 is 6
LCM of denominators i.e. for 384,624 is 4992.
Thus, GCF of Fractions is 6/4992.Finally, GCF of Fractions for 1968/384, 4746/624 is 6/4992.