GCF of 7428/67, 3444/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7428/67, 3444/978 i.e 12/65526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7428/67, 3444/978.
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 7428/67,3444/978?
Given fractions are 7428/67,3444/978
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 7428/67,3444/978, numerators are 7428,3444
Denominators are 67,978
The GCF of 7428,3444 is 12 .
LCM of 67,978 is 65526.
The greatest common factor of 7428/67,3444/978 = [GCF of 7428,3444]/[LCM of 67,978]= 12/65526
Therefore, the GCF of 7428/67,3444/978 is 12/65526.
To find the highest common factor of 7428,3444, we have to find the factors of both numbers and list the highest common factor.
The factors of 7428 are 1, 2, 3, 4, 6, 12, 619, 1238, 1857, 2476, 3714, 7428
The factors of 3444 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 41, 42, 82, 84, 123, 164, 246, 287, 492, 574, 861, 1148, 1722, 3444
The HCF of 7428,3444 is 12.
Lets's calculate GCF of 7428,3444
| 2 | 7428, 3444 |
| 2 | 3714, 1722 |
| 3 | 1857, 861 |
| 619, 287 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 7428,3444 By Matching Biggest Common Factor Method
Now, list down the factors of 7428
:1,2,3,4,6,12,619,1238,1857,2476,3714,7428
Now, list down the factors of 3444
:1,2,3,4,6,7,12,14,21,28,41,42,82,84,123,164,246,287,492,574,861,1148,1722,3444
Greatest Common Factor
We found the factors 7428,3444 . The biggest common factor number is the GCF number.
So the greatest common factor 7428,3444 is 12.
Lets's calculate LCM of 67,978
Given numbers has no common factors except 1. So, there LCM is their product i.e 65526
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/65526
Therefore, the GCF of Fractions 7428/67,3444/978 is 12/65526
Least Common Multiple of 67,978 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 67,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,978) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,978) x common factors =1 x 1 = 1
LCM(67,978) = ( 67 × 978 ) / 1
LCM(67,978) = 65526 / 1
LCM(67,978) = 65526
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FAQs on GCF of Fractions of 7428/67, 3444/978
1. What is the HCF of 7428,3444?
The HCF of 7428,3444 is 12
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 7428/67, 3444/978?
Answer: GCF of Numerators as per given numbers 7428/67, 3444/978 is
GCF of Numerators i.e. for 7428,3444 is 12
LCM of denominators i.e. for 67,978 is 65526.
Thus, GCF of Fractions is 12/65526.Finally, GCF of Fractions for 7428/67, 3444/978 is 12/65526.