GCF of 784/674, 612/410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 784/674, 612/410 i.e 4/138170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 784/674, 612/410.
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 784/674,612/410?
Given fractions are 784/674,612/410
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 784/674,612/410, numerators are 784,612
Denominators are 674,410
The GCF of 784,612 is 4 .
LCM of 674,410 is 138170.
The greatest common factor of 784/674,612/410 = [GCF of 784,612]/[LCM of 674,410]= 4/138170
Therefore, the GCF of 784/674,612/410 is 4/138170.
To find the highest common factor of 784,612, 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 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 784,612 is 4.
Lets's calculate GCF of 784,612
| 2 | 784, 612 |
| 2 | 392, 306 |
| 196, 153 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 784,612 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 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 784,612 . The biggest common factor number is the GCF number.
So the greatest common factor 784,612 is 4.
Lets's calculate LCM of 674,410
| 2 | 674, 410 |
| 337, 205 |
∴ So the LCM of the given numbers is 2 x 337 x 205 = 138170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/138170
Therefore, the GCF of Fractions 784/674,612/410 is 4/138170
Least Common Multiple of 674,410 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 674,410 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(674,410) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(674,410) x common factors =2 x 1 = 2
LCM(674,410) = ( 674 × 410 ) / 2
LCM(674,410) = 276340 / 2
LCM(674,410) = 138170
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FAQs on GCF of Fractions of 784/674, 612/410
1. What is the HCF of 784,612?
The HCF of 784,612 is 4
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 784/674, 612/410?
Answer: GCF of Numerators as per given numbers 784/674, 612/410 is
GCF of Numerators i.e. for 784,612 is 4
LCM of denominators i.e. for 674,410 is 138170.
Thus, GCF of Fractions is 4/138170.Finally, GCF of Fractions for 784/674, 612/410 is 4/138170.