GCF of 715/712, 9750/140
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 715/712, 9750/140 i.e 65/24920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 715/712, 9750/140.
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 715/712,9750/140?
Given fractions are 715/712,9750/140
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 715/712,9750/140, numerators are 715,9750
Denominators are 712,140
The GCF of 715,9750 is 65 .
LCM of 712,140 is 24920.
The greatest common factor of 715/712,9750/140 = [GCF of 715,9750]/[LCM of 712,140]= 65/24920
Therefore, the GCF of 715/712,9750/140 is 65/24920.
To find the highest common factor of 715,9750, we have to find the factors of both numbers and list the highest common factor.
The factors of 715 are 1, 5, 11, 13, 55, 65, 143, 715
The factors of 9750 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750
The HCF of 715,9750 is 65.
Lets's calculate GCF of 715,9750
| 5 | 715, 9750 |
| 13 | 143, 1950 |
| 11, 150 |
∴ So the GCF of the given numbers is 5 x 13 = 65
Greatest Common Factor of 715,9750 By Matching Biggest Common Factor Method
Now, list down the factors of 715
:1,5,11,13,55,65,143,715
Now, list down the factors of 9750
:1,2,3,5,6,10,13,15,25,26,30,39,50,65,75,78,125,130,150,195,250,325,375,390,650,750,975,1625,1950,3250,4875,9750
Greatest Common Factor
We found the factors 715,9750 . The biggest common factor number is the GCF number.
So the greatest common factor 715,9750 is 65.
Lets's calculate LCM of 712,140
| 2 | 712, 140 |
| 2 | 356, 70 |
| 178, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 178 x 35 = 24920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 65/24920
Therefore, the GCF of Fractions 715/712,9750/140 is 65/24920
Least Common Multiple of 712,140 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 712,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(712,140) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(712,140) x common factors =4 x 1 = 4
LCM(712,140) = ( 712 × 140 ) / 4
LCM(712,140) = 99680 / 4
LCM(712,140) = 24920
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FAQs on GCF of Fractions of 715/712, 9750/140
1. What is the HCF of 715,9750?
The HCF of 715,9750 is 65
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 715/712, 9750/140?
Answer: GCF of Numerators as per given numbers 715/712, 9750/140 is
GCF of Numerators i.e. for 715,9750 is 65
LCM of denominators i.e. for 712,140 is 24920.
Thus, GCF of Fractions is 65/24920.Finally, GCF of Fractions for 715/712, 9750/140 is 65/24920.