GCF of 2142/312, 3762/1160
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2142/312, 3762/1160 i.e 18/45240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2142/312, 3762/1160.
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 2142/312,3762/1160?
Given fractions are 2142/312,3762/1160
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 2142/312,3762/1160, numerators are 2142,3762
Denominators are 312,1160
The GCF of 2142,3762 is 18 .
LCM of 312,1160 is 45240.
The greatest common factor of 2142/312,3762/1160 = [GCF of 2142,3762]/[LCM of 312,1160]= 18/45240
Therefore, the GCF of 2142/312,3762/1160 is 18/45240.
To find the highest common factor of 2142,3762, we have to find the factors of both numbers and list the highest common factor.
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 factors of 3762 are 1, 2, 3, 6, 9, 11, 18, 19, 22, 33, 38, 57, 66, 99, 114, 171, 198, 209, 342, 418, 627, 1254, 1881, 3762
The HCF of 2142,3762 is 18.
Lets's calculate GCF of 2142,3762
| 2 | 2142, 3762 |
| 3 | 1071, 1881 |
| 3 | 357, 627 |
| 119, 209 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 2142,3762 By Matching Biggest Common Factor Method
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
Now, list down the factors of 3762
:1,2,3,6,9,11,18,19,22,33,38,57,66,99,114,171,198,209,342,418,627,1254,1881,3762
Greatest Common Factor
We found the factors 2142,3762 . The biggest common factor number is the GCF number.
So the greatest common factor 2142,3762 is 18.
Lets's calculate LCM of 312,1160
| 2 | 312, 1160 |
| 2 | 156, 580 |
| 2 | 78, 290 |
| 39, 145 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 39 x 145 = 45240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/45240
Therefore, the GCF of Fractions 2142/312,3762/1160 is 18/45240
Least Common Multiple of 312,1160 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 312,1160 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,1160) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(312,1160) x common factors =8 x 1 = 8
LCM(312,1160) = ( 312 × 1160 ) / 8
LCM(312,1160) = 361920 / 8
LCM(312,1160) = 45240
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FAQs on GCF of Fractions of 2142/312, 3762/1160
1. What is the HCF of 2142,3762?
The HCF of 2142,3762 is 18
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 2142/312, 3762/1160?
Answer: GCF of Numerators as per given numbers 2142/312, 3762/1160 is
GCF of Numerators i.e. for 2142,3762 is 18
LCM of denominators i.e. for 312,1160 is 45240.
Thus, GCF of Fractions is 18/45240.Finally, GCF of Fractions for 2142/312, 3762/1160 is 18/45240.