GCF of 852/998, 768/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 852/998, 768/840 i.e 12/419160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/998, 768/840.
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 852/998,768/840?
Given fractions are 852/998,768/840
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 852/998,768/840, numerators are 852,768
Denominators are 998,840
The GCF of 852,768 is 12 .
LCM of 998,840 is 419160.
The greatest common factor of 852/998,768/840 = [GCF of 852,768]/[LCM of 998,840]= 12/419160
Therefore, the GCF of 852/998,768/840 is 12/419160.
To find the highest common factor of 852,768, 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 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 852,768 is 12.
Lets's calculate GCF of 852,768
| 2 | 852, 768 |
| 2 | 426, 384 |
| 3 | 213, 192 |
| 71, 64 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 852,768 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 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 852,768 . The biggest common factor number is the GCF number.
So the greatest common factor 852,768 is 12.
Lets's calculate LCM of 998,840
| 2 | 998, 840 |
| 499, 420 |
∴ So the LCM of the given numbers is 2 x 499 x 420 = 419160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/419160
Therefore, the GCF of Fractions 852/998,768/840 is 12/419160
Least Common Multiple of 998,840 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 998,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(998,840) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(998,840) x common factors =2 x 1 = 2
LCM(998,840) = ( 998 × 840 ) / 2
LCM(998,840) = 838320 / 2
LCM(998,840) = 419160
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 852/998, 768/840
1. What is the HCF of 852,768?
The HCF of 852,768 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 852/998, 768/840?
Answer: GCF of Numerators as per given numbers 852/998, 768/840 is
GCF of Numerators i.e. for 852,768 is 12
LCM of denominators i.e. for 998,840 is 419160.
Thus, GCF of Fractions is 12/419160.Finally, GCF of Fractions for 852/998, 768/840 is 12/419160.