GCF of 780/463, 312/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 780/463, 312/412 i.e 156/190756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/463, 312/412.
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 780/463,312/412?
Given fractions are 780/463,312/412
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 780/463,312/412, numerators are 780,312
Denominators are 463,412
The GCF of 780,312 is 156 .
LCM of 463,412 is 190756.
The greatest common factor of 780/463,312/412 = [GCF of 780,312]/[LCM of 463,412]= 156/190756
Therefore, the GCF of 780/463,312/412 is 156/190756.
To find the highest common factor of 780,312, we have to find the factors of both numbers and list the highest common factor.
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 factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 780,312 is 156.
Lets's calculate GCF of 780,312
| 2 | 780, 312 |
| 2 | 390, 156 |
| 3 | 195, 78 |
| 13 | 65, 26 |
| 5, 2 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 13 = 156
Greatest Common Factor of 780,312 By Matching Biggest Common Factor Method
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
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 780,312 . The biggest common factor number is the GCF number.
So the greatest common factor 780,312 is 156.
Lets's calculate LCM of 463,412
Given numbers has no common factors except 1. So, there LCM is their product i.e 190756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 156/190756
Therefore, the GCF of Fractions 780/463,312/412 is 156/190756
Least Common Multiple of 463,412 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 463,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(463,412) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(463,412) x common factors =1 x 1 = 1
LCM(463,412) = ( 463 × 412 ) / 1
LCM(463,412) = 190756 / 1
LCM(463,412) = 190756
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FAQs on GCF of Fractions of 780/463, 312/412
1. What is the HCF of 780,312?
The HCF of 780,312 is 156
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 780/463, 312/412?
Answer: GCF of Numerators as per given numbers 780/463, 312/412 is
GCF of Numerators i.e. for 780,312 is 156
LCM of denominators i.e. for 463,412 is 190756.
Thus, GCF of Fractions is 156/190756.Finally, GCF of Fractions for 780/463, 312/412 is 156/190756.