GCF of 688/383, 344/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 688/383, 344/728 i.e 344/278824 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/383, 344/728.
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 688/383,344/728?
Given fractions are 688/383,344/728
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 688/383,344/728, numerators are 688,344
Denominators are 383,728
The GCF of 688,344 is 344 .
LCM of 383,728 is 278824.
The greatest common factor of 688/383,344/728 = [GCF of 688,344]/[LCM of 383,728]= 344/278824
Therefore, the GCF of 688/383,344/728 is 344/278824.
To find the highest common factor of 688,344, we have to find the factors of both numbers and list the highest common factor.
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The HCF of 688,344 is 344.
Lets's calculate GCF of 688,344
| 2 | 688, 344 |
| 2 | 344, 172 |
| 2 | 86, 172 |
| 43 | 43, 86 |
| 1, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 43 = 344
Greatest Common Factor of 688,344 By Matching Biggest Common Factor Method
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Greatest Common Factor
We found the factors 688,344 . The biggest common factor number is the GCF number.
So the greatest common factor 688,344 is 344.
Lets's calculate LCM of 383,728
Given numbers has no common factors except 1. So, there LCM is their product i.e 278824
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 344/278824
Therefore, the GCF of Fractions 688/383,344/728 is 344/278824
Least Common Multiple of 383,728 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 383,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(383,728) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(383,728) x common factors =1 x 1 = 1
LCM(383,728) = ( 383 × 728 ) / 1
LCM(383,728) = 278824 / 1
LCM(383,728) = 278824
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FAQs on GCF of Fractions of 688/383, 344/728
1. What is the HCF of 688,344?
The HCF of 688,344 is 344
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 688/383, 344/728?
Answer: GCF of Numerators as per given numbers 688/383, 344/728 is
GCF of Numerators i.e. for 688,344 is 344
LCM of denominators i.e. for 383,728 is 278824.
Thus, GCF of Fractions is 344/278824.Finally, GCF of Fractions for 688/383, 344/728 is 344/278824.