GCF of 1022/219, 2176/2139
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1022/219, 2176/2139 i.e 2/156147 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1022/219, 2176/2139.
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 1022/219,2176/2139?
Given fractions are 1022/219,2176/2139
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 1022/219,2176/2139, numerators are 1022,2176
Denominators are 219,2139
The GCF of 1022,2176 is 2 .
LCM of 219,2139 is 156147.
The greatest common factor of 1022/219,2176/2139 = [GCF of 1022,2176]/[LCM of 219,2139]= 2/156147
Therefore, the GCF of 1022/219,2176/2139 is 2/156147.
To find the highest common factor of 1022,2176, we have to find the factors of both numbers and list the highest common factor.
The factors of 1022 are 1, 2, 7, 14, 73, 146, 511, 1022
The factors of 2176 are 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 128, 136, 272, 544, 1088, 2176
The HCF of 1022,2176 is 2.
Lets's calculate GCF of 1022,2176
| 2 | 1022, 2176 |
| 511, 1088 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1022,2176 By Matching Biggest Common Factor Method
Now, list down the factors of 1022
:1,2,7,14,73,146,511,1022
Now, list down the factors of 2176
:1,2,4,8,16,17,32,34,64,68,128,136,272,544,1088,2176
Greatest Common Factor
We found the factors 1022,2176 . The biggest common factor number is the GCF number.
So the greatest common factor 1022,2176 is 2.
Lets's calculate LCM of 219,2139
| 3 | 219, 2139 |
| 73, 713 |
∴ So the LCM of the given numbers is 3 x 73 x 713 = 156147
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/156147
Therefore, the GCF of Fractions 1022/219,2176/2139 is 2/156147
Least Common Multiple of 219,2139 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 219,2139 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,2139) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,2139) x common factors =3 x 1 = 3
LCM(219,2139) = ( 219 × 2139 ) / 3
LCM(219,2139) = 468441 / 3
LCM(219,2139) = 156147
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FAQs on GCF of Fractions of 1022/219, 2176/2139
1. What is the HCF of 1022,2176?
The HCF of 1022,2176 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 1022/219, 2176/2139?
Answer: GCF of Numerators as per given numbers 1022/219, 2176/2139 is
GCF of Numerators i.e. for 1022,2176 is 2
LCM of denominators i.e. for 219,2139 is 156147.
Thus, GCF of Fractions is 2/156147.Finally, GCF of Fractions for 1022/219, 2176/2139 is 2/156147.