GCF of 7658/295, 2142/4300
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7658/295, 2142/4300 i.e 14/253700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7658/295, 2142/4300.
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 7658/295,2142/4300?
Given fractions are 7658/295,2142/4300
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 7658/295,2142/4300, numerators are 7658,2142
Denominators are 295,4300
The GCF of 7658,2142 is 14 .
LCM of 295,4300 is 253700.
The greatest common factor of 7658/295,2142/4300 = [GCF of 7658,2142]/[LCM of 295,4300]= 14/253700
Therefore, the GCF of 7658/295,2142/4300 is 14/253700.
To find the highest common factor of 7658,2142, we have to find the factors of both numbers and list the highest common factor.
The factors of 7658 are 1, 2, 7, 14, 547, 1094, 3829, 7658
The factors of 2142 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142
The HCF of 7658,2142 is 14.
Lets's calculate GCF of 7658,2142
| 2 | 7658, 2142 |
| 7 | 3829, 1071 |
| 547, 153 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 7658,2142 By Matching Biggest Common Factor Method
Now, list down the factors of 7658
:1,2,7,14,547,1094,3829,7658
Now, list down the factors of 2142
:1,2,3,6,7,9,14,17,18,21,34,42,51,63,102,119,126,153,238,306,357,714,1071,2142
Greatest Common Factor
We found the factors 7658,2142 . The biggest common factor number is the GCF number.
So the greatest common factor 7658,2142 is 14.
Lets's calculate LCM of 295,4300
| 5 | 295, 4300 |
| 59, 860 |
∴ So the LCM of the given numbers is 5 x 59 x 860 = 253700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/253700
Therefore, the GCF of Fractions 7658/295,2142/4300 is 14/253700
Least Common Multiple of 295,4300 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 295,4300 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(295,4300) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(295,4300) x common factors =5 x 1 = 5
LCM(295,4300) = ( 295 × 4300 ) / 5
LCM(295,4300) = 1268500 / 5
LCM(295,4300) = 253700
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FAQs on GCF of Fractions of 7658/295, 2142/4300
1. What is the HCF of 7658,2142?
The HCF of 7658,2142 is 14
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 7658/295, 2142/4300?
Answer: GCF of Numerators as per given numbers 7658/295, 2142/4300 is
GCF of Numerators i.e. for 7658,2142 is 14
LCM of denominators i.e. for 295,4300 is 253700.
Thus, GCF of Fractions is 14/253700.Finally, GCF of Fractions for 7658/295, 2142/4300 is 14/253700.