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GCF of 564/78, 692/523

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 564/78, 692/523 i.e 4/40794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/78, 692/523.

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 564/78,692/523?

Given fractions are 564/78,692/523

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 564/78,692/523, numerators are 564,692

Denominators are 78,523

The GCF of 564,692 is 4 .

LCM of 78,523 is 40794.

The greatest common factor of 564/78,692/523 = [GCF of 564,692]/[LCM of 78,523]= 4/40794

Therefore, the GCF of 564/78,692/523 is 4/40794.

Greatest Common Factor of 564,692

To find the highest common factor of 564,692, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 692 are 1, 2, 4, 173, 346, 692

The HCF of 564,692 is 4.

Lets's calculate GCF of 564,692

Greatest Common Factor (GCF) of 564,692 By Common Division

2 564, 692
2 282, 346
141, 173

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 564,692 By Matching Biggest Common Factor Method

Greatest Common Factor of 564,692 By Matching Biggest Common Factor Method

Now, list down the factors of 564

:

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

Now, list down the factors of 692

:

1,2,4,173,346,692

Greatest Common Factor

We found the factors 564,692 . The biggest common factor number is the GCF number.
So the greatest common factor 564,692 is 4.

Lets's calculate LCM of 78,523

Lowest Common Multiple of 78,523 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 40794

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/40794

Therefore, the GCF of Fractions 564/78,692/523 is 4/40794

Least Common Multiple of 78,523 with GCF Formula

Least Common Multiple of 78,523 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 78,523 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,523) = 1

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

GCF(78,523) x common factors =1 x 1 = 1

LCM(78,523) = ( 78 × 523 ) / 1

LCM(78,523) = 40794 / 1

LCM(78,523) = 40794


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FAQs on GCF of Fractions of 564/78, 692/523

1. What is the HCF of 564,692?

The HCF of 564,692 is 4

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 564/78, 692/523?

Answer: GCF of Numerators as per given numbers 564/78, 692/523 is

GCF of Numerators i.e. for 564,692 is 4

LCM of denominators i.e. for 78,523 is 40794.

Thus, GCF of Fractions is 4/40794.Finally, GCF of Fractions for 564/78, 692/523 is 4/40794.