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GCF of 186/17, 234/1561

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 186/17, 234/1561 i.e 6/26537 easily. The following is the detailed procedure to determine the greatest common factor of fractions 186/17, 234/1561.

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 186/17,234/1561?

Given fractions are 186/17,234/1561

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 186/17,234/1561, numerators are 186,234

Denominators are 17,1561

The GCF of 186,234 is 6 .

LCM of 17,1561 is 26537.

The greatest common factor of 186/17,234/1561 = [GCF of 186,234]/[LCM of 17,1561]= 6/26537

Therefore, the GCF of 186/17,234/1561 is 6/26537.

Greatest Common Factor of 186,234

To find the highest common factor of 186,234, we have to find the factors of both numbers and list the highest common factor.

The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186

The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234

The HCF of 186,234 is 6.

Lets's calculate GCF of 186,234

Greatest Common Factor (GCF) of 186,234 By Common Division

2 186, 234
3 93, 117
31, 39

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 186,234 By Matching Biggest Common Factor Method

Greatest Common Factor of 186,234 By Matching Biggest Common Factor Method

Now, list down the factors of 186

:

1,2,3,6,31,62,93,186

Now, list down the factors of 234

:

1,2,3,6,9,13,18,26,39,78,117,234

Greatest Common Factor

We found the factors 186,234 . The biggest common factor number is the GCF number.
So the greatest common factor 186,234 is 6.

Lets's calculate LCM of 17,1561

Lowest Common Multiple of 17,1561 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 26537

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/26537

Therefore, the GCF of Fractions 186/17,234/1561 is 6/26537

Least Common Multiple of 17,1561 with GCF Formula

Least Common Multiple of 17,1561 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 17,1561 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,1561) = 1

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

GCF(17,1561) x common factors =1 x 1 = 1

LCM(17,1561) = ( 17 × 1561 ) / 1

LCM(17,1561) = 26537 / 1

LCM(17,1561) = 26537


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FAQs on GCF of Fractions of 186/17, 234/1561

1. What is the HCF of 186,234?

The HCF of 186,234 is 6

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 186/17, 234/1561?

Answer: GCF of Numerators as per given numbers 186/17, 234/1561 is

GCF of Numerators i.e. for 186,234 is 6

LCM of denominators i.e. for 17,1561 is 26537.

Thus, GCF of Fractions is 6/26537.Finally, GCF of Fractions for 186/17, 234/1561 is 6/26537.