GCF of 195/75, 630/340
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 195/75, 630/340 i.e 15/5100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 195/75, 630/340.
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 195/75,630/340?
Given fractions are 195/75,630/340
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 195/75,630/340, numerators are 195,630
Denominators are 75,340
The GCF of 195,630 is 15 .
LCM of 75,340 is 5100.
The greatest common factor of 195/75,630/340 = [GCF of 195,630]/[LCM of 75,340]= 15/5100
Therefore, the GCF of 195/75,630/340 is 15/5100.
To find the highest common factor of 195,630, we have to find the factors of both numbers and list the highest common factor.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195
The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
The HCF of 195,630 is 15.
Lets's calculate GCF of 195,630
| 3 | 195, 630 |
| 5 | 65, 210 |
| 13, 42 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 195,630 By Matching Biggest Common Factor Method
Now, list down the factors of 195
:1,3,5,13,15,39,65,195
Now, list down the factors of 630
:1,2,3,5,6,7,9,10,14,15,18,21,30,35,42,45,63,70,90,105,126,210,315,630
Greatest Common Factor
We found the factors 195,630 . The biggest common factor number is the GCF number.
So the greatest common factor 195,630 is 15.
Lets's calculate LCM of 75,340
| 5 | 75, 340 |
| 15, 68 |
∴ So the LCM of the given numbers is 5 x 15 x 68 = 5100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/5100
Therefore, the GCF of Fractions 195/75,630/340 is 15/5100
Least Common Multiple of 75,340 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 75,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,340) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(75,340) x common factors =5 x 1 = 5
LCM(75,340) = ( 75 × 340 ) / 5
LCM(75,340) = 25500 / 5
LCM(75,340) = 5100
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FAQs on GCF of Fractions of 195/75, 630/340
1. What is the HCF of 195,630?
The HCF of 195,630 is 15
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 195/75, 630/340?
Answer: GCF of Numerators as per given numbers 195/75, 630/340 is
GCF of Numerators i.e. for 195,630 is 15
LCM of denominators i.e. for 75,340 is 5100.
Thus, GCF of Fractions is 15/5100.Finally, GCF of Fractions for 195/75, 630/340 is 15/5100.