GCF of 315/746, 420/213
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/746, 420/213 i.e 105/158898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/746, 420/213.
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 315/746,420/213?
Given fractions are 315/746,420/213
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 315/746,420/213, numerators are 315,420
Denominators are 746,213
The GCF of 315,420 is 105 .
LCM of 746,213 is 158898.
The greatest common factor of 315/746,420/213 = [GCF of 315,420]/[LCM of 746,213]= 105/158898
Therefore, the GCF of 315/746,420/213 is 105/158898.
To find the highest common factor of 315,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 315,420 is 105.
Lets's calculate GCF of 315,420
| 3 | 315, 420 |
| 5 | 105, 140 |
| 7 | 21, 28 |
| 3, 4 |
∴ So the GCF of the given numbers is 3 x 5 x 7 = 105
Greatest Common Factor of 315,420 By Matching Biggest Common Factor Method
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 315,420 . The biggest common factor number is the GCF number.
So the greatest common factor 315,420 is 105.
Lets's calculate LCM of 746,213
Given numbers has no common factors except 1. So, there LCM is their product i.e 158898
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 105/158898
Therefore, the GCF of Fractions 315/746,420/213 is 105/158898
Least Common Multiple of 746,213 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 746,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(746,213) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(746,213) x common factors =1 x 1 = 1
LCM(746,213) = ( 746 × 213 ) / 1
LCM(746,213) = 158898 / 1
LCM(746,213) = 158898
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FAQs on GCF of Fractions of 315/746, 420/213
1. What is the HCF of 315,420?
The HCF of 315,420 is 105
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 315/746, 420/213?
Answer: GCF of Numerators as per given numbers 315/746, 420/213 is
GCF of Numerators i.e. for 315,420 is 105
LCM of denominators i.e. for 746,213 is 158898.
Thus, GCF of Fractions is 105/158898.Finally, GCF of Fractions for 315/746, 420/213 is 105/158898.