How to Find GCF of 72/77, 512/13, 608/760?

GCF of 72/77, 512/13, 608/760

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 72/77, 512/13, 608/760 i.e 8/760760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/77, 512/13, 608/760.

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 72/77,512/13,608/760?

Given fractions are 72/77,512/13,608/760

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 72/77,512/13,608/760, numerators are 72,512,608

Denominators are 77,13,760

The GCF of 72,512,608 is 8 .

LCM of 77,13,760 is 760760.

The greatest common factor of 72/77,512/13,608/760 = [GCF of 72,512,608]/[LCM of 77,13,760]= 8/760760

Therefore, the GCF of 72/77,512/13,608/760 is 8/760760.

Greatest Common Factor of 72,512,608

To find the highest common factor of 72,512,608, we have to find the factors of both numbers and list the highest common factor.

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608

The HCF of 72,512,608 is 8.

Lets's calculate GCF of 72,512,608

Greatest Common Factor (GCF) of 72,512,608 By Common Division

2	72, 512, 608
2	36, 256, 304
2	18, 128, 152
	9, 64, 76

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 72,512,608 By Matching Biggest Common Factor Method

Now, list down the factors of 72

1,2,3,4,6,8,9,12,18,24,36,72

Now, list down the factors of 512

1,2,4,8,16,32,64,128,256,512

Now, list down the factors of 608

1,2,4,8,16,19,32,38,76,152,304,608

Greatest Common Factor

We found the factors 72,512,608 . The biggest common factor number is the GCF number.
So the greatest common factor 72,512,608 is 8.

Lets's calculate LCM of 77,13,760

Lowest Common Multiple of 77,13,760 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 760760

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/760760

Therefore, the GCF of Fractions 72/77,512/13,608/760 is 8/760760

Least Common Multiple of 77,13,760 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 77,13,760 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,13,760) = 1

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

GCF(77,13,760) x common factors =1 x 1 = 1

LCM(77,13,760) = ( 77 × 13 × 760 ) / 1

LCM(77,13,760) = 760760 / 1

LCM(77,13,760) = 760760

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FAQs on GCF of Fractions of 72/77, 512/13, 608/760

1. What is the HCF of 72,512,608?

The HCF of 72,512,608 is 8

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 72/77, 512/13, 608/760?

Answer: GCF of Numerators as per given numbers 72/77, 512/13, 608/760 is

GCF of Numerators i.e. for 72,512,608 is 8

LCM of denominators i.e. for 77,13,760 is 760760.

Thus, GCF of Fractions is 8/760760.Finally, GCF of Fractions for 72/77, 512/13, 608/760 is 8/760760.