GCF of 9174/429, 1978/8114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9174/429, 1978/8114 i.e 2/3480906 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9174/429, 1978/8114.
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 9174/429,1978/8114?
Given fractions are 9174/429,1978/8114
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 9174/429,1978/8114, numerators are 9174,1978
Denominators are 429,8114
The GCF of 9174,1978 is 2 .
LCM of 429,8114 is 3480906.
The greatest common factor of 9174/429,1978/8114 = [GCF of 9174,1978]/[LCM of 429,8114]= 2/3480906
Therefore, the GCF of 9174/429,1978/8114 is 2/3480906.
To find the highest common factor of 9174,1978, we have to find the factors of both numbers and list the highest common factor.
The factors of 9174 are 1, 2, 3, 6, 11, 22, 33, 66, 139, 278, 417, 834, 1529, 3058, 4587, 9174
The factors of 1978 are 1, 2, 23, 43, 46, 86, 989, 1978
The HCF of 9174,1978 is 2.
Lets's calculate GCF of 9174,1978
| 2 | 9174, 1978 |
| 4587, 989 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 9174,1978 By Matching Biggest Common Factor Method
Now, list down the factors of 9174
:1,2,3,6,11,22,33,66,139,278,417,834,1529,3058,4587,9174
Now, list down the factors of 1978
:1,2,23,43,46,86,989,1978
Greatest Common Factor
We found the factors 9174,1978 . The biggest common factor number is the GCF number.
So the greatest common factor 9174,1978 is 2.
Lets's calculate LCM of 429,8114
Given numbers has no common factors except 1. So, there LCM is their product i.e 3480906
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3480906
Therefore, the GCF of Fractions 9174/429,1978/8114 is 2/3480906
Least Common Multiple of 429,8114 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 429,8114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(429,8114) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(429,8114) x common factors =1 x 1 = 1
LCM(429,8114) = ( 429 × 8114 ) / 1
LCM(429,8114) = 3480906 / 1
LCM(429,8114) = 3480906
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FAQs on GCF of Fractions of 9174/429, 1978/8114
1. What is the HCF of 9174,1978?
The HCF of 9174,1978 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 9174/429, 1978/8114?
Answer: GCF of Numerators as per given numbers 9174/429, 1978/8114 is
GCF of Numerators i.e. for 9174,1978 is 2
LCM of denominators i.e. for 429,8114 is 3480906.
Thus, GCF of Fractions is 2/3480906.Finally, GCF of Fractions for 9174/429, 1978/8114 is 2/3480906.