GCF of 4142/738, 4978/6692
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4142/738, 4978/6692 i.e 38/2469348 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4142/738, 4978/6692.
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 4142/738,4978/6692?
Given fractions are 4142/738,4978/6692
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 4142/738,4978/6692, numerators are 4142,4978
Denominators are 738,6692
The GCF of 4142,4978 is 38 .
LCM of 738,6692 is 2469348.
The greatest common factor of 4142/738,4978/6692 = [GCF of 4142,4978]/[LCM of 738,6692]= 38/2469348
Therefore, the GCF of 4142/738,4978/6692 is 38/2469348.
To find the highest common factor of 4142,4978, we have to find the factors of both numbers and list the highest common factor.
The factors of 4142 are 1, 2, 19, 38, 109, 218, 2071, 4142
The factors of 4978 are 1, 2, 19, 38, 131, 262, 2489, 4978
The HCF of 4142,4978 is 38.
Lets's calculate GCF of 4142,4978
| 2 | 4142, 4978 |
| 19 | 2071, 2489 |
| 109, 131 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 4142,4978 By Matching Biggest Common Factor Method
Now, list down the factors of 4142
:1,2,19,38,109,218,2071,4142
Now, list down the factors of 4978
:1,2,19,38,131,262,2489,4978
Greatest Common Factor
We found the factors 4142,4978 . The biggest common factor number is the GCF number.
So the greatest common factor 4142,4978 is 38.
Lets's calculate LCM of 738,6692
| 2 | 738, 6692 |
| 369, 3346 |
∴ So the LCM of the given numbers is 2 x 369 x 3346 = 2469348
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/2469348
Therefore, the GCF of Fractions 4142/738,4978/6692 is 38/2469348
Least Common Multiple of 738,6692 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 738,6692 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(738,6692) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(738,6692) x common factors =2 x 1 = 2
LCM(738,6692) = ( 738 × 6692 ) / 2
LCM(738,6692) = 4938696 / 2
LCM(738,6692) = 2469348
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FAQs on GCF of Fractions of 4142/738, 4978/6692
1. What is the HCF of 4142,4978?
The HCF of 4142,4978 is 38
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 4142/738, 4978/6692?
Answer: GCF of Numerators as per given numbers 4142/738, 4978/6692 is
GCF of Numerators i.e. for 4142,4978 is 38
LCM of denominators i.e. for 738,6692 is 2469348.
Thus, GCF of Fractions is 38/2469348.Finally, GCF of Fractions for 4142/738, 4978/6692 is 38/2469348.