GCF of 822/767, 864/342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 822/767, 864/342 i.e 6/262314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 822/767, 864/342.
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 822/767,864/342?
Given fractions are 822/767,864/342
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 822/767,864/342, numerators are 822,864
Denominators are 767,342
The GCF of 822,864 is 6 .
LCM of 767,342 is 262314.
The greatest common factor of 822/767,864/342 = [GCF of 822,864]/[LCM of 767,342]= 6/262314
Therefore, the GCF of 822/767,864/342 is 6/262314.
To find the highest common factor of 822,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 822,864 is 6.
Lets's calculate GCF of 822,864
| 2 | 822, 864 |
| 3 | 411, 432 |
| 137, 144 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 822,864 By Matching Biggest Common Factor Method
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 822,864 . The biggest common factor number is the GCF number.
So the greatest common factor 822,864 is 6.
Lets's calculate LCM of 767,342
Given numbers has no common factors except 1. So, there LCM is their product i.e 262314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/262314
Therefore, the GCF of Fractions 822/767,864/342 is 6/262314
Least Common Multiple of 767,342 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 767,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(767,342) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(767,342) x common factors =1 x 1 = 1
LCM(767,342) = ( 767 × 342 ) / 1
LCM(767,342) = 262314 / 1
LCM(767,342) = 262314
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FAQs on GCF of Fractions of 822/767, 864/342
1. What is the HCF of 822,864?
The HCF of 822,864 is 6
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 822/767, 864/342?
Answer: GCF of Numerators as per given numbers 822/767, 864/342 is
GCF of Numerators i.e. for 822,864 is 6
LCM of denominators i.e. for 767,342 is 262314.
Thus, GCF of Fractions is 6/262314.Finally, GCF of Fractions for 822/767, 864/342 is 6/262314.