GCF of 3180/420, 1412/1178
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3180/420, 1412/1178 i.e 4/247380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3180/420, 1412/1178.
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 3180/420,1412/1178?
Given fractions are 3180/420,1412/1178
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 3180/420,1412/1178, numerators are 3180,1412
Denominators are 420,1178
The GCF of 3180,1412 is 4 .
LCM of 420,1178 is 247380.
The greatest common factor of 3180/420,1412/1178 = [GCF of 3180,1412]/[LCM of 420,1178]= 4/247380
Therefore, the GCF of 3180/420,1412/1178 is 4/247380.
To find the highest common factor of 3180,1412, we have to find the factors of both numbers and list the highest common factor.
The factors of 3180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 53, 60, 106, 159, 212, 265, 318, 530, 636, 795, 1060, 1590, 3180
The factors of 1412 are 1, 2, 4, 353, 706, 1412
The HCF of 3180,1412 is 4.
Lets's calculate GCF of 3180,1412
| 2 | 3180, 1412 |
| 2 | 1590, 706 |
| 795, 353 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 3180,1412 By Matching Biggest Common Factor Method
Now, list down the factors of 3180
:1,2,3,4,5,6,10,12,15,20,30,53,60,106,159,212,265,318,530,636,795,1060,1590,3180
Now, list down the factors of 1412
:1,2,4,353,706,1412
Greatest Common Factor
We found the factors 3180,1412 . The biggest common factor number is the GCF number.
So the greatest common factor 3180,1412 is 4.
Lets's calculate LCM of 420,1178
| 2 | 420, 1178 |
| 210, 589 |
∴ So the LCM of the given numbers is 2 x 210 x 589 = 247380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/247380
Therefore, the GCF of Fractions 3180/420,1412/1178 is 4/247380
Least Common Multiple of 420,1178 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 420,1178 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,1178) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(420,1178) x common factors =2 x 1 = 2
LCM(420,1178) = ( 420 × 1178 ) / 2
LCM(420,1178) = 494760 / 2
LCM(420,1178) = 247380
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 3180/420, 1412/1178
1. What is the HCF of 3180,1412?
The HCF of 3180,1412 is 4
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 3180/420, 1412/1178?
Answer: GCF of Numerators as per given numbers 3180/420, 1412/1178 is
GCF of Numerators i.e. for 3180,1412 is 4
LCM of denominators i.e. for 420,1178 is 247380.
Thus, GCF of Fractions is 4/247380.Finally, GCF of Fractions for 3180/420, 1412/1178 is 4/247380.