GCF of 217/974, 6510/786
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 217/974, 6510/786 i.e 217/382782 easily. The following is the detailed procedure to determine the greatest common factor of fractions 217/974, 6510/786.
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 217/974,6510/786?
Given fractions are 217/974,6510/786
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 217/974,6510/786, numerators are 217,6510
Denominators are 974,786
The GCF of 217,6510 is 217 .
LCM of 974,786 is 382782.
The greatest common factor of 217/974,6510/786 = [GCF of 217,6510]/[LCM of 974,786]= 217/382782
Therefore, the GCF of 217/974,6510/786 is 217/382782.
To find the highest common factor of 217,6510, we have to find the factors of both numbers and list the highest common factor.
The factors of 217 are 1, 7, 31, 217
The factors of 6510 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 31, 35, 42, 62, 70, 93, 105, 155, 186, 210, 217, 310, 434, 465, 651, 930, 1085, 1302, 2170, 3255, 6510
The HCF of 217,6510 is 217.
Lets's calculate GCF of 217,6510
| 7 | 217, 6510 |
| 31 | 31, 930 |
| 1, 30 |
∴ So the GCF of the given numbers is 7 x 31 = 217
Greatest Common Factor of 217,6510 By Matching Biggest Common Factor Method
Now, list down the factors of 217
:1,7,31,217
Now, list down the factors of 6510
:1,2,3,5,6,7,10,14,15,21,30,31,35,42,62,70,93,105,155,186,210,217,310,434,465,651,930,1085,1302,2170,3255,6510
Greatest Common Factor
We found the factors 217,6510 . The biggest common factor number is the GCF number.
So the greatest common factor 217,6510 is 217.
Lets's calculate LCM of 974,786
| 2 | 974, 786 |
| 487, 393 |
∴ So the LCM of the given numbers is 2 x 487 x 393 = 382782
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 217/382782
Therefore, the GCF of Fractions 217/974,6510/786 is 217/382782
Least Common Multiple of 974,786 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 974,786 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(974,786) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(974,786) x common factors =2 x 1 = 2
LCM(974,786) = ( 974 × 786 ) / 2
LCM(974,786) = 765564 / 2
LCM(974,786) = 382782
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FAQs on GCF of Fractions of 217/974, 6510/786
1. What is the HCF of 217,6510?
The HCF of 217,6510 is 217
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 217/974, 6510/786?
Answer: GCF of Numerators as per given numbers 217/974, 6510/786 is
GCF of Numerators i.e. for 217,6510 is 217
LCM of denominators i.e. for 974,786 is 382782.
Thus, GCF of Fractions is 217/382782.Finally, GCF of Fractions for 217/974, 6510/786 is 217/382782.