GCF of 852/312, 1860/766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 852/312, 1860/766 i.e 12/119496 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/312, 1860/766.
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 852/312,1860/766?
Given fractions are 852/312,1860/766
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 852/312,1860/766, numerators are 852,1860
Denominators are 312,766
The GCF of 852,1860 is 12 .
LCM of 312,766 is 119496.
The greatest common factor of 852/312,1860/766 = [GCF of 852,1860]/[LCM of 312,766]= 12/119496
Therefore, the GCF of 852/312,1860/766 is 12/119496.
To find the highest common factor of 852,1860, we have to find the factors of both numbers and list the highest common factor.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
The factors of 1860 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 31, 60, 62, 93, 124, 155, 186, 310, 372, 465, 620, 930, 1860
The HCF of 852,1860 is 12.
Lets's calculate GCF of 852,1860
| 2 | 852, 1860 |
| 2 | 426, 930 |
| 3 | 213, 465 |
| 71, 155 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 852,1860 By Matching Biggest Common Factor Method
Now, list down the factors of 852
:1,2,3,4,6,12,71,142,213,284,426,852
Now, list down the factors of 1860
:1,2,3,4,5,6,10,12,15,20,30,31,60,62,93,124,155,186,310,372,465,620,930,1860
Greatest Common Factor
We found the factors 852,1860 . The biggest common factor number is the GCF number.
So the greatest common factor 852,1860 is 12.
Lets's calculate LCM of 312,766
| 2 | 312, 766 |
| 156, 383 |
∴ So the LCM of the given numbers is 2 x 156 x 383 = 119496
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/119496
Therefore, the GCF of Fractions 852/312,1860/766 is 12/119496
Least Common Multiple of 312,766 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 312,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(312,766) x common factors =2 x 1 = 2
LCM(312,766) = ( 312 × 766 ) / 2
LCM(312,766) = 238992 / 2
LCM(312,766) = 119496
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FAQs on GCF of Fractions of 852/312, 1860/766
1. What is the HCF of 852,1860?
The HCF of 852,1860 is 12
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 852/312, 1860/766?
Answer: GCF of Numerators as per given numbers 852/312, 1860/766 is
GCF of Numerators i.e. for 852,1860 is 12
LCM of denominators i.e. for 312,766 is 119496.
Thus, GCF of Fractions is 12/119496.Finally, GCF of Fractions for 852/312, 1860/766 is 12/119496.