GCF of 784/164, 861/250
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/164, 861/250 i.e 7/20500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/164, 861/250.
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 784/164,861/250?
Given fractions are 784/164,861/250
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 784/164,861/250, numerators are 784,861
Denominators are 164,250
The GCF of 784,861 is 7 .
LCM of 164,250 is 20500.
The greatest common factor of 784/164,861/250 = [GCF of 784,861]/[LCM of 164,250]= 7/20500
Therefore, the GCF of 784/164,861/250 is 7/20500.
To find the highest common factor of 784,861, we have to find the factors of both numbers and list the highest common factor.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The factors of 861 are 1, 3, 7, 21, 41, 123, 287, 861
The HCF of 784,861 is 7.
Lets's calculate GCF of 784,861
| 7 | 784, 861 |
| 112, 123 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 784,861 By Matching Biggest Common Factor Method
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Now, list down the factors of 861
:1,3,7,21,41,123,287,861
Greatest Common Factor
We found the factors 784,861 . The biggest common factor number is the GCF number.
So the greatest common factor 784,861 is 7.
Lets's calculate LCM of 164,250
| 2 | 164, 250 |
| 82, 125 |
∴ So the LCM of the given numbers is 2 x 82 x 125 = 20500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/20500
Therefore, the GCF of Fractions 784/164,861/250 is 7/20500
Least Common Multiple of 164,250 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 164,250 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,250) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,250) x common factors =2 x 1 = 2
LCM(164,250) = ( 164 × 250 ) / 2
LCM(164,250) = 41000 / 2
LCM(164,250) = 20500
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FAQs on GCF of Fractions of 784/164, 861/250
1. What is the HCF of 784,861?
The HCF of 784,861 is 7
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 784/164, 861/250?
Answer: GCF of Numerators as per given numbers 784/164, 861/250 is
GCF of Numerators i.e. for 784,861 is 7
LCM of denominators i.e. for 164,250 is 20500.
Thus, GCF of Fractions is 7/20500.Finally, GCF of Fractions for 784/164, 861/250 is 7/20500.