GCF of 688/175, 312/635
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 688/175, 312/635 i.e 8/22225 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/175, 312/635.
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 688/175,312/635?
Given fractions are 688/175,312/635
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 688/175,312/635, numerators are 688,312
Denominators are 175,635
The GCF of 688,312 is 8 .
LCM of 175,635 is 22225.
The greatest common factor of 688/175,312/635 = [GCF of 688,312]/[LCM of 175,635]= 8/22225
Therefore, the GCF of 688/175,312/635 is 8/22225.
To find the highest common factor of 688,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 688,312 is 8.
Lets's calculate GCF of 688,312
| 2 | 688, 312 |
| 2 | 344, 156 |
| 2 | 172, 78 |
| 86, 39 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 688,312 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 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 688,312 . The biggest common factor number is the GCF number.
So the greatest common factor 688,312 is 8.
Lets's calculate LCM of 175,635
| 5 | 175, 635 |
| 35, 127 |
∴ So the LCM of the given numbers is 5 x 35 x 127 = 22225
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/22225
Therefore, the GCF of Fractions 688/175,312/635 is 8/22225
Least Common Multiple of 175,635 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 175,635 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(175,635) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(175,635) x common factors =5 x 1 = 5
LCM(175,635) = ( 175 × 635 ) / 5
LCM(175,635) = 111125 / 5
LCM(175,635) = 22225
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FAQs on GCF of Fractions of 688/175, 312/635
1. What is the HCF of 688,312?
The HCF of 688,312 is 8
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 688/175, 312/635?
Answer: GCF of Numerators as per given numbers 688/175, 312/635 is
GCF of Numerators i.e. for 688,312 is 8
LCM of denominators i.e. for 175,635 is 22225.
Thus, GCF of Fractions is 8/22225.Finally, GCF of Fractions for 688/175, 312/635 is 8/22225.