GCF of 674/784, 396/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 674/784, 396/420 i.e 2/11760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 674/784, 396/420.
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 674/784,396/420?
Given fractions are 674/784,396/420
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 674/784,396/420, numerators are 674,396
Denominators are 784,420
The GCF of 674,396 is 2 .
LCM of 784,420 is 11760.
The greatest common factor of 674/784,396/420 = [GCF of 674,396]/[LCM of 784,420]= 2/11760
Therefore, the GCF of 674/784,396/420 is 2/11760.
To find the highest common factor of 674,396, we have to find the factors of both numbers and list the highest common factor.
The factors of 674 are 1, 2, 337, 674
The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The HCF of 674,396 is 2.
Lets's calculate GCF of 674,396
| 2 | 674, 396 |
| 337, 198 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 674,396 By Matching Biggest Common Factor Method
Now, list down the factors of 674
:1,2,337,674
Now, list down the factors of 396
:1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Greatest Common Factor
We found the factors 674,396 . The biggest common factor number is the GCF number.
So the greatest common factor 674,396 is 2.
Lets's calculate LCM of 784,420
| 2 | 784, 420 |
| 2 | 392, 210 |
| 7 | 196, 105 |
| 28, 15 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 28 x 15 = 11760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11760
Therefore, the GCF of Fractions 674/784,396/420 is 2/11760
Least Common Multiple of 784,420 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 784,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(784,420) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(784,420) x common factors =28 x 1 = 28
LCM(784,420) = ( 784 × 420 ) / 28
LCM(784,420) = 329280 / 28
LCM(784,420) = 11760
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FAQs on GCF of Fractions of 674/784, 396/420
1. What is the HCF of 674,396?
The HCF of 674,396 is 2
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 674/784, 396/420?
Answer: GCF of Numerators as per given numbers 674/784, 396/420 is
GCF of Numerators i.e. for 674,396 is 2
LCM of denominators i.e. for 784,420 is 11760.
Thus, GCF of Fractions is 2/11760.Finally, GCF of Fractions for 674/784, 396/420 is 2/11760.