GCF of 7974/308, 8340/3687
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7974/308, 8340/3687 i.e 6/1135596 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7974/308, 8340/3687.
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 7974/308,8340/3687?
Given fractions are 7974/308,8340/3687
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 7974/308,8340/3687, numerators are 7974,8340
Denominators are 308,3687
The GCF of 7974,8340 is 6 .
LCM of 308,3687 is 1135596.
The greatest common factor of 7974/308,8340/3687 = [GCF of 7974,8340]/[LCM of 308,3687]= 6/1135596
Therefore, the GCF of 7974/308,8340/3687 is 6/1135596.
To find the highest common factor of 7974,8340, we have to find the factors of both numbers and list the highest common factor.
The factors of 7974 are 1, 2, 3, 6, 9, 18, 443, 886, 1329, 2658, 3987, 7974
The factors of 8340 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 139, 278, 417, 556, 695, 834, 1390, 1668, 2085, 2780, 4170, 8340
The HCF of 7974,8340 is 6.
Lets's calculate GCF of 7974,8340
| 2 | 7974, 8340 |
| 3 | 3987, 4170 |
| 1329, 1390 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 7974,8340 By Matching Biggest Common Factor Method
Now, list down the factors of 7974
:1,2,3,6,9,18,443,886,1329,2658,3987,7974
Now, list down the factors of 8340
:1,2,3,4,5,6,10,12,15,20,30,60,139,278,417,556,695,834,1390,1668,2085,2780,4170,8340
Greatest Common Factor
We found the factors 7974,8340 . The biggest common factor number is the GCF number.
So the greatest common factor 7974,8340 is 6.
Lets's calculate LCM of 308,3687
Given numbers has no common factors except 1. So, there LCM is their product i.e 1135596
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1135596
Therefore, the GCF of Fractions 7974/308,8340/3687 is 6/1135596
Least Common Multiple of 308,3687 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 308,3687 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(308,3687) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(308,3687) x common factors =1 x 1 = 1
LCM(308,3687) = ( 308 × 3687 ) / 1
LCM(308,3687) = 1135596 / 1
LCM(308,3687) = 1135596
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FAQs on GCF of Fractions of 7974/308, 8340/3687
1. What is the HCF of 7974,8340?
The HCF of 7974,8340 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 7974/308, 8340/3687?
Answer: GCF of Numerators as per given numbers 7974/308, 8340/3687 is
GCF of Numerators i.e. for 7974,8340 is 6
LCM of denominators i.e. for 308,3687 is 1135596.
Thus, GCF of Fractions is 6/1135596.Finally, GCF of Fractions for 7974/308, 8340/3687 is 6/1135596.