GCF of 480/643, 780/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 480/643, 780/684 i.e 60/439812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 480/643, 780/684.
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 480/643,780/684?
Given fractions are 480/643,780/684
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 480/643,780/684, numerators are 480,780
Denominators are 643,684
The GCF of 480,780 is 60 .
LCM of 643,684 is 439812.
The greatest common factor of 480/643,780/684 = [GCF of 480,780]/[LCM of 643,684]= 60/439812
Therefore, the GCF of 480/643,780/684 is 60/439812.
To find the highest common factor of 480,780, we have to find the factors of both numbers and list the highest common factor.
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780
The HCF of 480,780 is 60.
Lets's calculate GCF of 480,780
| 2 | 480, 780 |
| 2 | 240, 390 |
| 3 | 120, 195 |
| 5 | 40, 65 |
| 8, 13 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 480,780 By Matching Biggest Common Factor Method
Now, list down the factors of 480
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,80,96,120,160,240,480
Now, list down the factors of 780
:1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 480,780 . The biggest common factor number is the GCF number.
So the greatest common factor 480,780 is 60.
Lets's calculate LCM of 643,684
Given numbers has no common factors except 1. So, there LCM is their product i.e 439812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/439812
Therefore, the GCF of Fractions 480/643,780/684 is 60/439812
Least Common Multiple of 643,684 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 643,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(643,684) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(643,684) x common factors =1 x 1 = 1
LCM(643,684) = ( 643 × 684 ) / 1
LCM(643,684) = 439812 / 1
LCM(643,684) = 439812
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FAQs on GCF of Fractions of 480/643, 780/684
1. What is the HCF of 480,780?
The HCF of 480,780 is 60
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 480/643, 780/684?
Answer: GCF of Numerators as per given numbers 480/643, 780/684 is
GCF of Numerators i.e. for 480,780 is 60
LCM of denominators i.e. for 643,684 is 439812.
Thus, GCF of Fractions is 60/439812.Finally, GCF of Fractions for 480/643, 780/684 is 60/439812.