GCF of 685/30, 128/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 685/30, 128/400 i.e 1/1200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 685/30, 128/400.
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 685/30,128/400?
Given fractions are 685/30,128/400
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 685/30,128/400, numerators are 685,128
Denominators are 30,400
The GCF of 685,128 is 1 .
LCM of 30,400 is 1200.
The greatest common factor of 685/30,128/400 = [GCF of 685,128]/[LCM of 30,400]= 1/1200
Therefore, the GCF of 685/30,128/400 is 1/1200.
To find the highest common factor of 685,128, we have to find the factors of both numbers and list the highest common factor.
The factors of 685 are 1, 5, 137, 685
The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
The HCF of 685,128 is 1.
Lets's calculate GCF of 685,128
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 685,128 By Matching Biggest Common Factor Method
Now, list down the factors of 685
:1,5,137,685
Now, list down the factors of 128
:1,2,4,8,16,32,64,128
Greatest Common Factor
We found the factors 685,128 . The biggest common factor number is the GCF number.
So the greatest common factor 685,128 is 1.
Lets's calculate LCM of 30,400
| 2 | 30, 400 |
| 5 | 15, 200 |
| 3, 40 |
∴ So the LCM of the given numbers is 2 x 5 x 3 x 40 = 1200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1200
Therefore, the GCF of Fractions 685/30,128/400 is 1/1200
Least Common Multiple of 30,400 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 30,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,400) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(30,400) x common factors =10 x 1 = 10
LCM(30,400) = ( 30 × 400 ) / 10
LCM(30,400) = 12000 / 10
LCM(30,400) = 1200
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FAQs on GCF of Fractions of 685/30, 128/400
1. What is the HCF of 685,128?
The HCF of 685,128 is 1
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 685/30, 128/400?
Answer: GCF of Numerators as per given numbers 685/30, 128/400 is
GCF of Numerators i.e. for 685,128 is 1
LCM of denominators i.e. for 30,400 is 1200.
Thus, GCF of Fractions is 1/1200.Finally, GCF of Fractions for 685/30, 128/400 is 1/1200.