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GCF of 212/96, 109/570

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 212/96, 109/570 i.e 1/9120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 212/96, 109/570.

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 212/96,109/570?

Given fractions are 212/96,109/570

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 212/96,109/570, numerators are 212,109

Denominators are 96,570

The GCF of 212,109 is 1 .

LCM of 96,570 is 9120.

The greatest common factor of 212/96,109/570 = [GCF of 212,109]/[LCM of 96,570]= 1/9120

Therefore, the GCF of 212/96,109/570 is 1/9120.

Greatest Common Factor of 212,109

To find the highest common factor of 212,109, we have to find the factors of both numbers and list the highest common factor.

The factors of 212 are 1, 2, 4, 53, 106, 212

The factors of 109 are 1, 109

The HCF of 212,109 is 1.

Lets's calculate GCF of 212,109

Greatest Common Factor (GCF) of 212,109 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 212,109 By Matching Biggest Common Factor Method

Greatest Common Factor of 212,109 By Matching Biggest Common Factor Method

Now, list down the factors of 212

:

1,2,4,53,106,212

Now, list down the factors of 109

:

1,109

Greatest Common Factor

We found the factors 212,109 . The biggest common factor number is the GCF number.
So the greatest common factor 212,109 is 1.

Lets's calculate LCM of 96,570

Lowest Common Multiple of 96,570 using Common Division

2 96, 570
3 48, 285
16, 95

∴ So the LCM of the given numbers is 2 x 3 x 16 x 95 = 9120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9120

Therefore, the GCF of Fractions 212/96,109/570 is 1/9120

Least Common Multiple of 96,570 with GCF Formula

Least Common Multiple of 96,570 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 96,570 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(96,570) = 6

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

GCF(96,570) x common factors =6 x 1 = 6

LCM(96,570) = ( 96 × 570 ) / 6

LCM(96,570) = 54720 / 6

LCM(96,570) = 9120


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FAQs on GCF of Fractions of 212/96, 109/570

1. What is the HCF of 212,109?

The HCF of 212,109 is 1

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 212/96, 109/570?

Answer: GCF of Numerators as per given numbers 212/96, 109/570 is

GCF of Numerators i.e. for 212,109 is 1

LCM of denominators i.e. for 96,570 is 9120.

Thus, GCF of Fractions is 1/9120.Finally, GCF of Fractions for 212/96, 109/570 is 1/9120.