GCF of 1053/212, 5670/282
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1053/212, 5670/282 i.e 81/29892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1053/212, 5670/282.
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 1053/212,5670/282?
Given fractions are 1053/212,5670/282
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 1053/212,5670/282, numerators are 1053,5670
Denominators are 212,282
The GCF of 1053,5670 is 81 .
LCM of 212,282 is 29892.
The greatest common factor of 1053/212,5670/282 = [GCF of 1053,5670]/[LCM of 212,282]= 81/29892
Therefore, the GCF of 1053/212,5670/282 is 81/29892.
To find the highest common factor of 1053,5670, we have to find the factors of both numbers and list the highest common factor.
The factors of 1053 are 1, 3, 9, 13, 27, 39, 81, 117, 351, 1053
The factors of 5670 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 81, 90, 105, 126, 135, 162, 189, 210, 270, 315, 378, 405, 567, 630, 810, 945, 1134, 1890, 2835, 5670
The HCF of 1053,5670 is 81.
Lets's calculate GCF of 1053,5670
| 3 | 1053, 5670 |
| 3 | 351, 1890 |
| 3 | 117, 630 |
| 3 | 39, 210 |
| 13, 70 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 3 = 81
Greatest Common Factor of 1053,5670 By Matching Biggest Common Factor Method
Now, list down the factors of 1053
:1,3,9,13,27,39,81,117,351,1053
Now, list down the factors of 5670
:1,2,3,5,6,7,9,10,14,15,18,21,27,30,35,42,45,54,63,70,81,90,105,126,135,162,189,210,270,315,378,405,567,630,810,945,1134,1890,2835,5670
Greatest Common Factor
We found the factors 1053,5670 . The biggest common factor number is the GCF number.
So the greatest common factor 1053,5670 is 81.
Lets's calculate LCM of 212,282
| 2 | 212, 282 |
| 106, 141 |
∴ So the LCM of the given numbers is 2 x 106 x 141 = 29892
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 81/29892
Therefore, the GCF of Fractions 1053/212,5670/282 is 81/29892
Least Common Multiple of 212,282 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 212,282 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,282) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(212,282) x common factors =2 x 1 = 2
LCM(212,282) = ( 212 × 282 ) / 2
LCM(212,282) = 59784 / 2
LCM(212,282) = 29892
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FAQs on GCF of Fractions of 1053/212, 5670/282
1. What is the HCF of 1053,5670?
The HCF of 1053,5670 is 81
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 1053/212, 5670/282?
Answer: GCF of Numerators as per given numbers 1053/212, 5670/282 is
GCF of Numerators i.e. for 1053,5670 is 81
LCM of denominators i.e. for 212,282 is 29892.
Thus, GCF of Fractions is 81/29892.Finally, GCF of Fractions for 1053/212, 5670/282 is 81/29892.