GCF of 7674/214, 7208/9847
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7674/214, 7208/9847 i.e 2/2107258 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7674/214, 7208/9847.
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 7674/214,7208/9847?
Given fractions are 7674/214,7208/9847
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 7674/214,7208/9847, numerators are 7674,7208
Denominators are 214,9847
The GCF of 7674,7208 is 2 .
LCM of 214,9847 is 2107258.
The greatest common factor of 7674/214,7208/9847 = [GCF of 7674,7208]/[LCM of 214,9847]= 2/2107258
Therefore, the GCF of 7674/214,7208/9847 is 2/2107258.
To find the highest common factor of 7674,7208, we have to find the factors of both numbers and list the highest common factor.
The factors of 7674 are 1, 2, 3, 6, 1279, 2558, 3837, 7674
The factors of 7208 are 1, 2, 4, 8, 17, 34, 53, 68, 106, 136, 212, 424, 901, 1802, 3604, 7208
The HCF of 7674,7208 is 2.
Lets's calculate GCF of 7674,7208
| 2 | 7674, 7208 |
| 3837, 3604 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7674,7208 By Matching Biggest Common Factor Method
Now, list down the factors of 7674
:1,2,3,6,1279,2558,3837,7674
Now, list down the factors of 7208
:1,2,4,8,17,34,53,68,106,136,212,424,901,1802,3604,7208
Greatest Common Factor
We found the factors 7674,7208 . The biggest common factor number is the GCF number.
So the greatest common factor 7674,7208 is 2.
Lets's calculate LCM of 214,9847
Given numbers has no common factors except 1. So, there LCM is their product i.e 2107258
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2107258
Therefore, the GCF of Fractions 7674/214,7208/9847 is 2/2107258
Least Common Multiple of 214,9847 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 214,9847 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,9847) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,9847) x common factors =1 x 1 = 1
LCM(214,9847) = ( 214 × 9847 ) / 1
LCM(214,9847) = 2107258 / 1
LCM(214,9847) = 2107258
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FAQs on GCF of Fractions of 7674/214, 7208/9847
1. What is the HCF of 7674,7208?
The HCF of 7674,7208 is 2
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 7674/214, 7208/9847?
Answer: GCF of Numerators as per given numbers 7674/214, 7208/9847 is
GCF of Numerators i.e. for 7674,7208 is 2
LCM of denominators i.e. for 214,9847 is 2107258.
Thus, GCF of Fractions is 2/2107258.Finally, GCF of Fractions for 7674/214, 7208/9847 is 2/2107258.