GCF of 1646/778, 2142/859
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1646/778, 2142/859 i.e 2/668302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1646/778, 2142/859.
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 1646/778,2142/859?
Given fractions are 1646/778,2142/859
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 1646/778,2142/859, numerators are 1646,2142
Denominators are 778,859
The GCF of 1646,2142 is 2 .
LCM of 778,859 is 668302.
The greatest common factor of 1646/778,2142/859 = [GCF of 1646,2142]/[LCM of 778,859]= 2/668302
Therefore, the GCF of 1646/778,2142/859 is 2/668302.
To find the highest common factor of 1646,2142, we have to find the factors of both numbers and list the highest common factor.
The factors of 1646 are 1, 2, 823, 1646
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 1646,2142 is 2.
Lets's calculate GCF of 1646,2142
| 2 | 1646, 2142 |
| 823, 1071 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1646,2142 By Matching Biggest Common Factor Method
Now, list down the factors of 1646
:1,2,823,1646
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 1646,2142 . The biggest common factor number is the GCF number.
So the greatest common factor 1646,2142 is 2.
Lets's calculate LCM of 778,859
Given numbers has no common factors except 1. So, there LCM is their product i.e 668302
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/668302
Therefore, the GCF of Fractions 1646/778,2142/859 is 2/668302
Least Common Multiple of 778,859 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 778,859 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,859) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(778,859) x common factors =1 x 1 = 1
LCM(778,859) = ( 778 × 859 ) / 1
LCM(778,859) = 668302 / 1
LCM(778,859) = 668302
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FAQs on GCF of Fractions of 1646/778, 2142/859
1. What is the HCF of 1646,2142?
The HCF of 1646,2142 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 1646/778, 2142/859?
Answer: GCF of Numerators as per given numbers 1646/778, 2142/859 is
GCF of Numerators i.e. for 1646,2142 is 2
LCM of denominators i.e. for 778,859 is 668302.
Thus, GCF of Fractions is 2/668302.Finally, GCF of Fractions for 1646/778, 2142/859 is 2/668302.