GCF of 644/678, 9840/1687
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 644/678, 9840/1687 i.e 4/1143786 easily. The following is the detailed procedure to determine the greatest common factor of fractions 644/678, 9840/1687.
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 644/678,9840/1687?
Given fractions are 644/678,9840/1687
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 644/678,9840/1687, numerators are 644,9840
Denominators are 678,1687
The GCF of 644,9840 is 4 .
LCM of 678,1687 is 1143786.
The greatest common factor of 644/678,9840/1687 = [GCF of 644,9840]/[LCM of 678,1687]= 4/1143786
Therefore, the GCF of 644/678,9840/1687 is 4/1143786.
To find the highest common factor of 644,9840, we have to find the factors of both numbers and list the highest common factor.
The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644
The factors of 9840 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 41, 48, 60, 80, 82, 120, 123, 164, 205, 240, 246, 328, 410, 492, 615, 656, 820, 984, 1230, 1640, 1968, 2460, 3280, 4920, 9840
The HCF of 644,9840 is 4.
Lets's calculate GCF of 644,9840
| 2 | 644, 9840 |
| 2 | 322, 4920 |
| 161, 2460 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 644,9840 By Matching Biggest Common Factor Method
Now, list down the factors of 644
:1,2,4,7,14,23,28,46,92,161,322,644
Now, list down the factors of 9840
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,41,48,60,80,82,120,123,164,205,240,246,328,410,492,615,656,820,984,1230,1640,1968,2460,3280,4920,9840
Greatest Common Factor
We found the factors 644,9840 . The biggest common factor number is the GCF number.
So the greatest common factor 644,9840 is 4.
Lets's calculate LCM of 678,1687
Given numbers has no common factors except 1. So, there LCM is their product i.e 1143786
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1143786
Therefore, the GCF of Fractions 644/678,9840/1687 is 4/1143786
Least Common Multiple of 678,1687 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 678,1687 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,1687) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(678,1687) x common factors =1 x 1 = 1
LCM(678,1687) = ( 678 × 1687 ) / 1
LCM(678,1687) = 1143786 / 1
LCM(678,1687) = 1143786
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FAQs on GCF of Fractions of 644/678, 9840/1687
1. What is the HCF of 644,9840?
The HCF of 644,9840 is 4
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 644/678, 9840/1687?
Answer: GCF of Numerators as per given numbers 644/678, 9840/1687 is
GCF of Numerators i.e. for 644,9840 is 4
LCM of denominators i.e. for 678,1687 is 1143786.
Thus, GCF of Fractions is 4/1143786.Finally, GCF of Fractions for 644/678, 9840/1687 is 4/1143786.