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GCF of 210/28, 350/109

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 210/28, 350/109 i.e 70/3052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 210/28, 350/109.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 210/28,350/109?

Given fractions are 210/28,350/109

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 210/28,350/109, numerators are 210,350

Denominators are 28,109

The GCF of 210,350 is 70 .

LCM of 28,109 is 3052.

The greatest common factor of 210/28,350/109 = [GCF of 210,350]/[LCM of 28,109]= 70/3052

Therefore, the GCF of 210/28,350/109 is 70/3052.

Greatest Common Factor of 210,350

To find the highest common factor of 210,350, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350

The HCF of 210,350 is 70.

Lets's calculate GCF of 210,350

Greatest Common Factor (GCF) of 210,350 By Common Division

2 210, 350
5 105, 175
7 21, 35
3, 5

∴ So the GCF of the given numbers is 2 x 5 x 7 = 70

Greatest Common Factor of 210,350 By Matching Biggest Common Factor Method

Greatest Common Factor of 210,350 By Matching Biggest Common Factor Method

Now, list down the factors of 210

:

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

Now, list down the factors of 350

:

1,2,5,7,10,14,25,35,50,70,175,350

Greatest Common Factor

We found the factors 210,350 . The biggest common factor number is the GCF number.
So the greatest common factor 210,350 is 70.

Lets's calculate LCM of 28,109

Lowest Common Multiple of 28,109 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3052

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 70/3052

Therefore, the GCF of Fractions 210/28,350/109 is 70/3052

Least Common Multiple of 28,109 with GCF Formula

Least Common Multiple of 28,109 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 28,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(28,109) = 1

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

GCF(28,109) x common factors =1 x 1 = 1

LCM(28,109) = ( 28 × 109 ) / 1

LCM(28,109) = 3052 / 1

LCM(28,109) = 3052


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 210/28, 350/109

1. What is the HCF of 210,350?

The HCF of 210,350 is 70

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 210/28, 350/109?

Answer: GCF of Numerators as per given numbers 210/28, 350/109 is

GCF of Numerators i.e. for 210,350 is 70

LCM of denominators i.e. for 28,109 is 3052.

Thus, GCF of Fractions is 70/3052.Finally, GCF of Fractions for 210/28, 350/109 is 70/3052.