GCF of 920/67, 782/512
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 920/67, 782/512 i.e 46/34304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 920/67, 782/512.
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 920/67,782/512?
Given fractions are 920/67,782/512
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 920/67,782/512, numerators are 920,782
Denominators are 67,512
The GCF of 920,782 is 46 .
LCM of 67,512 is 34304.
The greatest common factor of 920/67,782/512 = [GCF of 920,782]/[LCM of 67,512]= 46/34304
Therefore, the GCF of 920/67,782/512 is 46/34304.
To find the highest common factor of 920,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 920 are 1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 920,782 is 46.
Lets's calculate GCF of 920,782
| 2 | 920, 782 |
| 23 | 460, 391 |
| 20, 17 |
∴ So the GCF of the given numbers is 2 x 23 = 46
Greatest Common Factor of 920,782 By Matching Biggest Common Factor Method
Now, list down the factors of 920
:1,2,4,5,8,10,20,23,40,46,92,115,184,230,460,920
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 920,782 . The biggest common factor number is the GCF number.
So the greatest common factor 920,782 is 46.
Lets's calculate LCM of 67,512
Given numbers has no common factors except 1. So, there LCM is their product i.e 34304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 46/34304
Therefore, the GCF of Fractions 920/67,782/512 is 46/34304
Least Common Multiple of 67,512 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 67,512 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(67,512) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(67,512) x common factors =1 x 1 = 1
LCM(67,512) = ( 67 × 512 ) / 1
LCM(67,512) = 34304 / 1
LCM(67,512) = 34304
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FAQs on GCF of Fractions of 920/67, 782/512
1. What is the HCF of 920,782?
The HCF of 920,782 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 920/67, 782/512?
Answer: GCF of Numerators as per given numbers 920/67, 782/512 is
GCF of Numerators i.e. for 920,782 is 46
LCM of denominators i.e. for 67,512 is 34304.
Thus, GCF of Fractions is 46/34304.Finally, GCF of Fractions for 920/67, 782/512 is 46/34304.