GCF of 5112/420, 2769/9114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5112/420, 2769/9114 i.e 213/91140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5112/420, 2769/9114.
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 5112/420,2769/9114?
Given fractions are 5112/420,2769/9114
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 5112/420,2769/9114, numerators are 5112,2769
Denominators are 420,9114
The GCF of 5112,2769 is 213 .
LCM of 420,9114 is 91140.
The greatest common factor of 5112/420,2769/9114 = [GCF of 5112,2769]/[LCM of 420,9114]= 213/91140
Therefore, the GCF of 5112/420,2769/9114 is 213/91140.
To find the highest common factor of 5112,2769, we have to find the factors of both numbers and list the highest common factor.
The factors of 5112 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 71, 72, 142, 213, 284, 426, 568, 639, 852, 1278, 1704, 2556, 5112
The factors of 2769 are 1, 3, 13, 39, 71, 213, 923, 2769
The HCF of 5112,2769 is 213.
Lets's calculate GCF of 5112,2769
| 3 | 5112, 2769 |
| 71 | 1704, 923 |
| 24, 13 |
∴ So the GCF of the given numbers is 3 x 71 = 213
Greatest Common Factor of 5112,2769 By Matching Biggest Common Factor Method
Now, list down the factors of 5112
:1,2,3,4,6,8,9,12,18,24,36,71,72,142,213,284,426,568,639,852,1278,1704,2556,5112
Now, list down the factors of 2769
:1,3,13,39,71,213,923,2769
Greatest Common Factor
We found the factors 5112,2769 . The biggest common factor number is the GCF number.
So the greatest common factor 5112,2769 is 213.
Lets's calculate LCM of 420,9114
| 2 | 420, 9114 |
| 3 | 210, 4557 |
| 7 | 70, 1519 |
| 10, 217 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 10 x 217 = 91140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 213/91140
Therefore, the GCF of Fractions 5112/420,2769/9114 is 213/91140
Least Common Multiple of 420,9114 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 420,9114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,9114) = 42
common factors(in case of two or more numbers have common factors) = 1
GCF(420,9114) x common factors =42 x 1 = 42
LCM(420,9114) = ( 420 × 9114 ) / 42
LCM(420,9114) = 3827880 / 42
LCM(420,9114) = 91140
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FAQs on GCF of Fractions of 5112/420, 2769/9114
1. What is the HCF of 5112,2769?
The HCF of 5112,2769 is 213
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 5112/420, 2769/9114?
Answer: GCF of Numerators as per given numbers 5112/420, 2769/9114 is
GCF of Numerators i.e. for 5112,2769 is 213
LCM of denominators i.e. for 420,9114 is 91140.
Thus, GCF of Fractions is 213/91140.Finally, GCF of Fractions for 5112/420, 2769/9114 is 213/91140.