GCF of 286/564, 688/376
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 286/564, 688/376 i.e 2/1128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/564, 688/376.
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 286/564,688/376?
Given fractions are 286/564,688/376
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 286/564,688/376, numerators are 286,688
Denominators are 564,376
The GCF of 286,688 is 2 .
LCM of 564,376 is 1128.
The greatest common factor of 286/564,688/376 = [GCF of 286,688]/[LCM of 564,376]= 2/1128
Therefore, the GCF of 286/564,688/376 is 2/1128.
To find the highest common factor of 286,688, we have to find the factors of both numbers and list the highest common factor.
The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The HCF of 286,688 is 2.
Lets's calculate GCF of 286,688
| 2 | 286, 688 |
| 143, 344 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 286,688 By Matching Biggest Common Factor Method
Now, list down the factors of 286
:1,2,11,13,22,26,143,286
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Greatest Common Factor
We found the factors 286,688 . The biggest common factor number is the GCF number.
So the greatest common factor 286,688 is 2.
Lets's calculate LCM of 564,376
| 2 | 564, 376 |
| 2 | 282, 188 |
| 47 | 141, 94 |
| 3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 47 x 3 x 2 = 1128
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1128
Therefore, the GCF of Fractions 286/564,688/376 is 2/1128
Least Common Multiple of 564,376 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 564,376 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,376) = 188
common factors(in case of two or more numbers have common factors) = 1
GCF(564,376) x common factors =188 x 1 = 188
LCM(564,376) = ( 564 × 376 ) / 188
LCM(564,376) = 212064 / 188
LCM(564,376) = 1128
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 286/564, 688/376
1. What is the HCF of 286,688?
The HCF of 286,688 is 2
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 286/564, 688/376?
Answer: GCF of Numerators as per given numbers 286/564, 688/376 is
GCF of Numerators i.e. for 286,688 is 2
LCM of denominators i.e. for 564,376 is 1128.
Thus, GCF of Fractions is 2/1128.Finally, GCF of Fractions for 286/564, 688/376 is 2/1128.