How to Find GCF of 315/47, 210/969?

GCF of 315/47, 210/969

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 315/47, 210/969 i.e 105/45543 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/47, 210/969.

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 315/47,210/969?

Given fractions are 315/47,210/969

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 315/47,210/969, numerators are 315,210

Denominators are 47,969

The GCF of 315,210 is 105 .

LCM of 47,969 is 45543.

The greatest common factor of 315/47,210/969 = [GCF of 315,210]/[LCM of 47,969]= 105/45543

Therefore, the GCF of 315/47,210/969 is 105/45543.

Greatest Common Factor of 315,210

To find the highest common factor of 315,210, 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 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 315,210 is 105.

Lets's calculate GCF of 315,210

Greatest Common Factor (GCF) of 315,210 By Common Division

3	315, 210
5	105, 70
7	21, 14
	3, 2

∴ So the GCF of the given numbers is 3 x 5 x 7 = 105

Greatest Common Factor of 315,210 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 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 315,210 . The biggest common factor number is the GCF number.
So the greatest common factor 315,210 is 105.

Lets's calculate LCM of 47,969

Lowest Common Multiple of 47,969 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 45543

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 105/45543

Therefore, the GCF of Fractions 315/47,210/969 is 105/45543

Least Common Multiple of 47,969 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 47,969 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(47,969) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(47,969) x common factors =1 x 1 = 1

LCM(47,969) = ( 47 × 969 ) / 1

LCM(47,969) = 45543 / 1

LCM(47,969) = 45543

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FAQs on GCF of Fractions of 315/47, 210/969

1. What is the HCF of 315,210?

The HCF of 315,210 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 315/47, 210/969?

Answer: GCF of Numerators as per given numbers 315/47, 210/969 is

GCF of Numerators i.e. for 315,210 is 105

LCM of denominators i.e. for 47,969 is 45543.

Thus, GCF of Fractions is 105/45543.Finally, GCF of Fractions for 315/47, 210/969 is 105/45543.