GCF of 140/450, 784/304
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 140/450, 784/304 i.e 28/68400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 140/450, 784/304.
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 140/450,784/304?
Given fractions are 140/450,784/304
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 140/450,784/304, numerators are 140,784
Denominators are 450,304
The GCF of 140,784 is 28 .
LCM of 450,304 is 68400.
The greatest common factor of 140/450,784/304 = [GCF of 140,784]/[LCM of 450,304]= 28/68400
Therefore, the GCF of 140/450,784/304 is 28/68400.
To find the highest common factor of 140,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 140,784 is 28.
Lets's calculate GCF of 140,784
| 2 | 140, 784 |
| 2 | 70, 392 |
| 7 | 35, 196 |
| 5, 28 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Greatest Common Factor of 140,784 By Matching Biggest Common Factor Method
Now, list down the factors of 140
:1,2,4,5,7,10,14,20,28,35,70,140
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 140,784 . The biggest common factor number is the GCF number.
So the greatest common factor 140,784 is 28.
Lets's calculate LCM of 450,304
| 2 | 450, 304 |
| 225, 152 |
∴ So the LCM of the given numbers is 2 x 225 x 152 = 68400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/68400
Therefore, the GCF of Fractions 140/450,784/304 is 28/68400
Least Common Multiple of 450,304 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 450,304 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(450,304) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(450,304) x common factors =2 x 1 = 2
LCM(450,304) = ( 450 × 304 ) / 2
LCM(450,304) = 136800 / 2
LCM(450,304) = 68400
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FAQs on GCF of Fractions of 140/450, 784/304
1. What is the HCF of 140,784?
The HCF of 140,784 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 140/450, 784/304?
Answer: GCF of Numerators as per given numbers 140/450, 784/304 is
GCF of Numerators i.e. for 140,784 is 28
LCM of denominators i.e. for 450,304 is 68400.
Thus, GCF of Fractions is 28/68400.Finally, GCF of Fractions for 140/450, 784/304 is 28/68400.