GCF of 894/414, 442/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 894/414, 442/762 i.e 2/52578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 894/414, 442/762.
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 894/414,442/762?
Given fractions are 894/414,442/762
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 894/414,442/762, numerators are 894,442
Denominators are 414,762
The GCF of 894,442 is 2 .
LCM of 414,762 is 52578.
The greatest common factor of 894/414,442/762 = [GCF of 894,442]/[LCM of 414,762]= 2/52578
Therefore, the GCF of 894/414,442/762 is 2/52578.
To find the highest common factor of 894,442, we have to find the factors of both numbers and list the highest common factor.
The factors of 894 are 1, 2, 3, 6, 149, 298, 447, 894
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The HCF of 894,442 is 2.
Lets's calculate GCF of 894,442
| 2 | 894, 442 |
| 447, 221 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 894,442 By Matching Biggest Common Factor Method
Now, list down the factors of 894
:1,2,3,6,149,298,447,894
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Greatest Common Factor
We found the factors 894,442 . The biggest common factor number is the GCF number.
So the greatest common factor 894,442 is 2.
Lets's calculate LCM of 414,762
| 2 | 414, 762 |
| 3 | 207, 381 |
| 69, 127 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 127 = 52578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/52578
Therefore, the GCF of Fractions 894/414,442/762 is 2/52578
Least Common Multiple of 414,762 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 414,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,762) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,762) x common factors =6 x 1 = 6
LCM(414,762) = ( 414 × 762 ) / 6
LCM(414,762) = 315468 / 6
LCM(414,762) = 52578
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FAQs on GCF of Fractions of 894/414, 442/762
1. What is the HCF of 894,442?
The HCF of 894,442 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 894/414, 442/762?
Answer: GCF of Numerators as per given numbers 894/414, 442/762 is
GCF of Numerators i.e. for 894,442 is 2
LCM of denominators i.e. for 414,762 is 52578.
Thus, GCF of Fractions is 2/52578.Finally, GCF of Fractions for 894/414, 442/762 is 2/52578.