How to Find GCF of 27/77, 896/10, 613/469?

GCF of 27/77, 896/10, 613/469

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 27/77, 896/10, 613/469 i.e 1/51590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/77, 896/10, 613/469.

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 27/77,896/10,613/469?

Given fractions are 27/77,896/10,613/469

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 27/77,896/10,613/469, numerators are 27,896,613

Denominators are 77,10,469

The GCF of 27,896,613 is 1 .

LCM of 77,10,469 is 51590.

The greatest common factor of 27/77,896/10,613/469 = [GCF of 27,896,613]/[LCM of 77,10,469]= 1/51590

Therefore, the GCF of 27/77,896/10,613/469 is 1/51590.

Greatest Common Factor of 27,896,613

To find the highest common factor of 27,896,613, we have to find the factors of both numbers and list the highest common factor.

The factors of 27 are 1, 3, 9, 27

The factors of 896 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896

The factors of 613 are 1, 613

The HCF of 27,896,613 is 1.

Lets's calculate GCF of 27,896,613

Greatest Common Factor (GCF) of 27,896,613 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 27,896,613 By Matching Biggest Common Factor Method

Now, list down the factors of 27

1,3,9,27

Now, list down the factors of 896

1,2,4,7,8,14,16,28,32,56,64,112,128,224,448,896

Now, list down the factors of 613

1,613

Greatest Common Factor

We found the factors 27,896,613 . The biggest common factor number is the GCF number.
So the greatest common factor 27,896,613 is 1.

Lets's calculate LCM of 77,10,469

Lowest Common Multiple of 77,10,469 using Common Division

7	77, 10, 469
	11, 10, 67

∴ So the LCM of the given numbers is 7 x 11 x 10 x 67 = 51590

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51590

Therefore, the GCF of Fractions 27/77,896/10,613/469 is 1/51590

Least Common Multiple of 77,10,469 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 77,10,469 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(77,10,469) = 1

common factors(in case of two or more numbers have common factors) = 7

GCF(77,10,469) x common factors =1 x 7 = 7

LCM(77,10,469) = ( 77 × 10 × 469 ) / 7

LCM(77,10,469) = 361130 / 7

LCM(77,10,469) = 51590

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 27/77, 896/10, 613/469

1. What is the HCF of 27,896,613?

The HCF of 27,896,613 is 1

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 27/77, 896/10, 613/469?

Answer: GCF of Numerators as per given numbers 27/77, 896/10, 613/469 is

GCF of Numerators i.e. for 27,896,613 is 1

LCM of denominators i.e. for 77,10,469 is 51590.

Thus, GCF of Fractions is 1/51590.Finally, GCF of Fractions for 27/77, 896/10, 613/469 is 1/51590.