GCF of 9688/67, 9408/997
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9688/67, 9408/997 i.e 56/66799 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9688/67, 9408/997.
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 9688/67,9408/997?
Given fractions are 9688/67,9408/997
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 9688/67,9408/997, numerators are 9688,9408
Denominators are 67,997
The GCF of 9688,9408 is 56 .
LCM of 67,997 is 66799.
The greatest common factor of 9688/67,9408/997 = [GCF of 9688,9408]/[LCM of 67,997]= 56/66799
Therefore, the GCF of 9688/67,9408/997 is 56/66799.
To find the highest common factor of 9688,9408, we have to find the factors of both numbers and list the highest common factor.
The factors of 9688 are 1, 2, 4, 7, 8, 14, 28, 56, 173, 346, 692, 1211, 1384, 2422, 4844, 9688
The factors of 9408 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 64, 84, 96, 98, 112, 147, 168, 192, 196, 224, 294, 336, 392, 448, 588, 672, 784, 1176, 1344, 1568, 2352, 3136, 4704, 9408
The HCF of 9688,9408 is 56.
Lets's calculate GCF of 9688,9408
| 2 | 9688, 9408 |
| 2 | 4844, 4704 |
| 2 | 2422, 2352 |
| 7 | 1211, 1176 |
| 173, 168 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56
Greatest Common Factor of 9688,9408 By Matching Biggest Common Factor Method
Now, list down the factors of 9688
:1,2,4,7,8,14,28,56,173,346,692,1211,1384,2422,4844,9688
Now, list down the factors of 9408
:1,2,3,4,6,7,8,12,14,16,21,24,28,32,42,48,49,56,64,84,96,98,112,147,168,192,196,224,294,336,392,448,588,672,784,1176,1344,1568,2352,3136,4704,9408
Greatest Common Factor
We found the factors 9688,9408 . The biggest common factor number is the GCF number.
So the greatest common factor 9688,9408 is 56.
Lets's calculate LCM of 67,997
Given numbers has no common factors except 1. So, there LCM is their product i.e 66799
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/66799
Therefore, the GCF of Fractions 9688/67,9408/997 is 56/66799
Least Common Multiple of 67,997 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 67,997 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,997) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,997) x common factors =1 x 1 = 1
LCM(67,997) = ( 67 × 997 ) / 1
LCM(67,997) = 66799 / 1
LCM(67,997) = 66799
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FAQs on GCF of Fractions of 9688/67, 9408/997
1. What is the HCF of 9688,9408?
The HCF of 9688,9408 is 56
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 9688/67, 9408/997?
Answer: GCF of Numerators as per given numbers 9688/67, 9408/997 is
GCF of Numerators i.e. for 9688,9408 is 56
LCM of denominators i.e. for 67,997 is 66799.
Thus, GCF of Fractions is 56/66799.Finally, GCF of Fractions for 9688/67, 9408/997 is 56/66799.