GCF of 414/76, 920/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 414/76, 920/546 i.e 46/20748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 414/76, 920/546.
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 414/76,920/546?
Given fractions are 414/76,920/546
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 414/76,920/546, numerators are 414,920
Denominators are 76,546
The GCF of 414,920 is 46 .
LCM of 76,546 is 20748.
The greatest common factor of 414/76,920/546 = [GCF of 414,920]/[LCM of 76,546]= 46/20748
Therefore, the GCF of 414/76,920/546 is 46/20748.
To find the highest common factor of 414,920, we have to find the factors of both numbers and list the highest common factor.
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
The HCF of 414,920 is 46.
Lets's calculate GCF of 414,920
| 2 | 414, 920 |
| 23 | 207, 460 |
| 9, 20 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 414,920 By Matching Biggest Common Factor Method
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 920
:1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920
Greatest Common Factor
We found the factors 414,920 . The biggest common factor number is the GCF number.
So the greatest common factor 414,920 is 46.
Lets's calculate LCM of 76,546
| 2 | 76, 546 |
| 38, 273 |
∴ So the LCM of the given numbers is 2 x 38 x 273 = 20748
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/20748
Therefore, the GCF of Fractions 414/76,920/546 is 46/20748
Least Common Multiple of 76,546 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 76,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,546) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(76,546) x common factors =2 x 1 = 2
LCM(76,546) = ( 76 × 546 ) / 2
LCM(76,546) = 41496 / 2
LCM(76,546) = 20748
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FAQs on GCF of Fractions of 414/76, 920/546
1. What is the HCF of 414,920?
The HCF of 414,920 is 46
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 414/76, 920/546?
Answer: GCF of Numerators as per given numbers 414/76, 920/546 is
GCF of Numerators i.e. for 414,920 is 46
LCM of denominators i.e. for 76,546 is 20748.
Thus, GCF of Fractions is 46/20748.Finally, GCF of Fractions for 414/76, 920/546 is 46/20748.