How to Find GCF of 77/864, 4466/8188?

GCF of 77/864, 4466/8188

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 77/864, 4466/8188 i.e 77/1768608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/864, 4466/8188.

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 77/864,4466/8188?

Given fractions are 77/864,4466/8188

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 77/864,4466/8188, numerators are 77,4466

Denominators are 864,8188

The GCF of 77,4466 is 77 .

LCM of 864,8188 is 1768608.

The greatest common factor of 77/864,4466/8188 = [GCF of 77,4466]/[LCM of 864,8188]= 77/1768608

Therefore, the GCF of 77/864,4466/8188 is 77/1768608.

Greatest Common Factor of 77,4466

To find the highest common factor of 77,4466, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 4466 are 1, 2, 7, 11, 14, 22, 29, 58, 77, 154, 203, 319, 406, 638, 2233, 4466

The HCF of 77,4466 is 77.

Lets's calculate GCF of 77,4466

Greatest Common Factor (GCF) of 77,4466 By Common Division

7	77, 4466
11	11, 638
	1, 58

∴ So the GCF of the given numbers is 7 x 11 = 77

Greatest Common Factor of 77,4466 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 4466

1,2,7,11,14,22,29,58,77,154,203,319,406,638,2233,4466

Greatest Common Factor

We found the factors 77,4466 . The biggest common factor number is the GCF number.
So the greatest common factor 77,4466 is 77.

Lets's calculate LCM of 864,8188

Lowest Common Multiple of 864,8188 using Common Division

2	864, 8188
2	432, 4094
	216, 2047

∴ So the LCM of the given numbers is 2 x 2 x 216 x 2047 = 1768608

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 77/1768608

Therefore, the GCF of Fractions 77/864,4466/8188 is 77/1768608

Least Common Multiple of 864,8188 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 864,8188 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(864,8188) = 4

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

GCF(864,8188) x common factors =4 x 1 = 4

LCM(864,8188) = ( 864 × 8188 ) / 4

LCM(864,8188) = 7074432 / 4

LCM(864,8188) = 1768608

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FAQs on GCF of Fractions of 77/864, 4466/8188

1. What is the HCF of 77,4466?

The HCF of 77,4466 is 77

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 77/864, 4466/8188?

Answer: GCF of Numerators as per given numbers 77/864, 4466/8188 is

GCF of Numerators i.e. for 77,4466 is 77

LCM of denominators i.e. for 864,8188 is 1768608.

Thus, GCF of Fractions is 77/1768608.Finally, GCF of Fractions for 77/864, 4466/8188 is 77/1768608.