GCF of 784/183, 140/875
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/183, 140/875 i.e 28/160125 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/183, 140/875.
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 784/183,140/875?
Given fractions are 784/183,140/875
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 784/183,140/875, numerators are 784,140
Denominators are 183,875
The GCF of 784,140 is 28 .
LCM of 183,875 is 160125.
The greatest common factor of 784/183,140/875 = [GCF of 784,140]/[LCM of 183,875]= 28/160125
Therefore, the GCF of 784/183,140/875 is 28/160125.
To find the highest common factor of 784,140, 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 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The HCF of 784,140 is 28.
Lets's calculate GCF of 784,140
| 2 | 784, 140 |
| 2 | 392, 70 |
| 7 | 196, 35 |
| 28, 5 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 784,140 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 140
:1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 784,140 . The biggest common factor number is the GCF number.
So the greatest common factor 784,140 is 28.
Lets's calculate LCM of 183,875
Given numbers has no common factors except 1. So, there LCM is their product i.e 160125
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/160125
Therefore, the GCF of Fractions 784/183,140/875 is 28/160125
Least Common Multiple of 183,875 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 183,875 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(183,875) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(183,875) x common factors =1 x 1 = 1
LCM(183,875) = ( 183 × 875 ) / 1
LCM(183,875) = 160125 / 1
LCM(183,875) = 160125
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FAQs on GCF of Fractions of 784/183, 140/875
1. What is the HCF of 784,140?
The HCF of 784,140 is 28
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 784/183, 140/875?
Answer: GCF of Numerators as per given numbers 784/183, 140/875 is
GCF of Numerators i.e. for 784,140 is 28
LCM of denominators i.e. for 183,875 is 160125.
Thus, GCF of Fractions is 28/160125.Finally, GCF of Fractions for 784/183, 140/875 is 28/160125.