GCF of 7194/174, 7654/1068
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7194/174, 7654/1068 i.e 2/30972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7194/174, 7654/1068.
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 7194/174,7654/1068?
Given fractions are 7194/174,7654/1068
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 7194/174,7654/1068, numerators are 7194,7654
Denominators are 174,1068
The GCF of 7194,7654 is 2 .
LCM of 174,1068 is 30972.
The greatest common factor of 7194/174,7654/1068 = [GCF of 7194,7654]/[LCM of 174,1068]= 2/30972
Therefore, the GCF of 7194/174,7654/1068 is 2/30972.
To find the highest common factor of 7194,7654, we have to find the factors of both numbers and list the highest common factor.
The factors of 7194 are 1, 2, 3, 6, 11, 22, 33, 66, 109, 218, 327, 654, 1199, 2398, 3597, 7194
The factors of 7654 are 1, 2, 43, 86, 89, 178, 3827, 7654
The HCF of 7194,7654 is 2.
Lets's calculate GCF of 7194,7654
| 2 | 7194, 7654 |
| 3597, 3827 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7194,7654 By Matching Biggest Common Factor Method
Now, list down the factors of 7194
:1,2,3,6,11,22,33,66,109,218,327,654,1199,2398,3597,7194
Now, list down the factors of 7654
:1,2,43,86,89,178,3827,7654
Greatest Common Factor
We found the factors 7194,7654 . The biggest common factor number is the GCF number.
So the greatest common factor 7194,7654 is 2.
Lets's calculate LCM of 174,1068
| 2 | 174, 1068 |
| 3 | 87, 534 |
| 29, 178 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 178 = 30972
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30972
Therefore, the GCF of Fractions 7194/174,7654/1068 is 2/30972
Least Common Multiple of 174,1068 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 174,1068 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(174,1068) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(174,1068) x common factors =6 x 1 = 6
LCM(174,1068) = ( 174 × 1068 ) / 6
LCM(174,1068) = 185832 / 6
LCM(174,1068) = 30972
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FAQs on GCF of Fractions of 7194/174, 7654/1068
1. What is the HCF of 7194,7654?
The HCF of 7194,7654 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 7194/174, 7654/1068?
Answer: GCF of Numerators as per given numbers 7194/174, 7654/1068 is
GCF of Numerators i.e. for 7194,7654 is 2
LCM of denominators i.e. for 174,1068 is 30972.
Thus, GCF of Fractions is 2/30972.Finally, GCF of Fractions for 7194/174, 7654/1068 is 2/30972.