How to Find GCF of 189/856, 3437/752?

GCF of 189/856, 3437/752

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 189/856, 3437/752 i.e 7/80464 easily. The following is the detailed procedure to determine the greatest common factor of fractions 189/856, 3437/752.

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 189/856,3437/752?

Given fractions are 189/856,3437/752

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 189/856,3437/752, numerators are 189,3437

Denominators are 856,752

The GCF of 189,3437 is 7 .

LCM of 856,752 is 80464.

The greatest common factor of 189/856,3437/752 = [GCF of 189,3437]/[LCM of 856,752]= 7/80464

Therefore, the GCF of 189/856,3437/752 is 7/80464.

Greatest Common Factor of 189,3437

To find the highest common factor of 189,3437, we have to find the factors of both numbers and list the highest common factor.

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The factors of 3437 are 1, 7, 491, 3437

The HCF of 189,3437 is 7.

Lets's calculate GCF of 189,3437

Greatest Common Factor (GCF) of 189,3437 By Common Division

7	189, 3437
	27, 491

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 189,3437 By Matching Biggest Common Factor Method

Now, list down the factors of 189

1,3,7,9,21,27,63,189

Now, list down the factors of 3437

1,7,491,3437

Greatest Common Factor

We found the factors 189,3437 . The biggest common factor number is the GCF number.
So the greatest common factor 189,3437 is 7.

Lets's calculate LCM of 856,752

Lowest Common Multiple of 856,752 using Common Division

2	856, 752
2	428, 376
2	214, 188
	107, 94

∴ So the LCM of the given numbers is 2 x 2 x 2 x 107 x 94 = 80464

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/80464

Therefore, the GCF of Fractions 189/856,3437/752 is 7/80464

Least Common Multiple of 856,752 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 856,752 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(856,752) = 8

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

GCF(856,752) x common factors =8 x 1 = 8

LCM(856,752) = ( 856 × 752 ) / 8

LCM(856,752) = 643712 / 8

LCM(856,752) = 80464

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FAQs on GCF of Fractions of 189/856, 3437/752

1. What is the HCF of 189,3437?

The HCF of 189,3437 is 7

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 189/856, 3437/752?

Answer: GCF of Numerators as per given numbers 189/856, 3437/752 is

GCF of Numerators i.e. for 189,3437 is 7

LCM of denominators i.e. for 856,752 is 80464.

Thus, GCF of Fractions is 7/80464.Finally, GCF of Fractions for 189/856, 3437/752 is 7/80464.