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GCF of 156/54, 564/289

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 156/54, 564/289 i.e 12/15606 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/54, 564/289.

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 156/54,564/289?

Given fractions are 156/54,564/289

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 156/54,564/289, numerators are 156,564

Denominators are 54,289

The GCF of 156,564 is 12 .

LCM of 54,289 is 15606.

The greatest common factor of 156/54,564/289 = [GCF of 156,564]/[LCM of 54,289]= 12/15606

Therefore, the GCF of 156/54,564/289 is 12/15606.

Greatest Common Factor of 156,564

To find the highest common factor of 156,564, we have to find the factors of both numbers and list the highest common factor.

The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

The HCF of 156,564 is 12.

Lets's calculate GCF of 156,564

Greatest Common Factor (GCF) of 156,564 By Common Division

2 156, 564
2 78, 282
3 39, 141
13, 47

∴ So the GCF of the given numbers is 2 x 2 x 3 = 12

Greatest Common Factor of 156,564 By Matching Biggest Common Factor Method

Greatest Common Factor of 156,564 By Matching Biggest Common Factor Method

Now, list down the factors of 156

:

1,2,3,4,6,12,13,26,39,52,78,156

Now, list down the factors of 564

:

1,2,3,4,6,12,47,94,141,188,282,564

Greatest Common Factor

We found the factors 156,564 . The biggest common factor number is the GCF number.
So the greatest common factor 156,564 is 12.

Lets's calculate LCM of 54,289

Lowest Common Multiple of 54,289 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 15606

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/15606

Therefore, the GCF of Fractions 156/54,564/289 is 12/15606

Least Common Multiple of 54,289 with GCF Formula

Least Common Multiple of 54,289 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 54,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,289) = 1

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

GCF(54,289) x common factors =1 x 1 = 1

LCM(54,289) = ( 54 × 289 ) / 1

LCM(54,289) = 15606 / 1

LCM(54,289) = 15606


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FAQs on GCF of Fractions of 156/54, 564/289

1. What is the HCF of 156,564?

The HCF of 156,564 is 12

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 156/54, 564/289?

Answer: GCF of Numerators as per given numbers 156/54, 564/289 is

GCF of Numerators i.e. for 156,564 is 12

LCM of denominators i.e. for 54,289 is 15606.

Thus, GCF of Fractions is 12/15606.Finally, GCF of Fractions for 156/54, 564/289 is 12/15606.