GCF of 1785/705, 5970/651
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1785/705, 5970/651 i.e 15/152985 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1785/705, 5970/651.
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 1785/705,5970/651?
Given fractions are 1785/705,5970/651
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 1785/705,5970/651, numerators are 1785,5970
Denominators are 705,651
The GCF of 1785,5970 is 15 .
LCM of 705,651 is 152985.
The greatest common factor of 1785/705,5970/651 = [GCF of 1785,5970]/[LCM of 705,651]= 15/152985
Therefore, the GCF of 1785/705,5970/651 is 15/152985.
To find the highest common factor of 1785,5970, we have to find the factors of both numbers and list the highest common factor.
The factors of 1785 are 1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595, 1785
The factors of 5970 are 1, 2, 3, 5, 6, 10, 15, 30, 199, 398, 597, 995, 1194, 1990, 2985, 5970
The HCF of 1785,5970 is 15.
Lets's calculate GCF of 1785,5970
| 3 | 1785, 5970 |
| 5 | 595, 1990 |
| 119, 398 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 1785,5970 By Matching Biggest Common Factor Method
Now, list down the factors of 1785
:1,3,5,7,15,17,21,35,51,85,105,119,255,357,595,1785
Now, list down the factors of 5970
:1,2,3,5,6,10,15,30,199,398,597,995,1194,1990,2985,5970
Greatest Common Factor
We found the factors 1785,5970 . The biggest common factor number is the GCF number.
So the greatest common factor 1785,5970 is 15.
Lets's calculate LCM of 705,651
| 3 | 705, 651 |
| 235, 217 |
∴ So the LCM of the given numbers is 3 x 235 x 217 = 152985
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/152985
Therefore, the GCF of Fractions 1785/705,5970/651 is 15/152985
Least Common Multiple of 705,651 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 705,651 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(705,651) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(705,651) x common factors =3 x 1 = 3
LCM(705,651) = ( 705 × 651 ) / 3
LCM(705,651) = 458955 / 3
LCM(705,651) = 152985
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FAQs on GCF of Fractions of 1785/705, 5970/651
1. What is the HCF of 1785,5970?
The HCF of 1785,5970 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 1785/705, 5970/651?
Answer: GCF of Numerators as per given numbers 1785/705, 5970/651 is
GCF of Numerators i.e. for 1785,5970 is 15
LCM of denominators i.e. for 705,651 is 152985.
Thus, GCF of Fractions is 15/152985.Finally, GCF of Fractions for 1785/705, 5970/651 is 15/152985.